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Journal articles on the topic 'Model of random process'

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Author: Grafiati

Published: 30 May 2022

Last updated: 31 May 2022

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1

Rudzitis, J., V. Padamans, E. Bordo, and R. Haytham. "Random process model of rough surfaces contact." Measurement Science and Technology 9, no. 7 (July 1, 1998): 1093–97. http://dx.doi.org/10.1088/0957-0233/9/7/015.

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2

Jiang, C., B. Y. Ni, N. Y. Liu, X. Han, and J. Liu. "Interval process model and non-random vibration analysis." Journal of Sound and Vibration 373 (July 2016): 104–31. http://dx.doi.org/10.1016/j.jsv.2016.03.019.

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3

Chen, Siyan, Yougui Wang, Keqiang Li, and Jinshan Wu. "Money creation process in a random redistribution model." Physica A: Statistical Mechanics and its Applications 394 (January 2014): 217–25. http://dx.doi.org/10.1016/j.physa.2013.09.036.

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4

Sanping Chen and S. Mills. "A binary Markov process model for random testing." IEEE Transactions on Software Engineering 22, no. 3 (March 1996): 218–23. http://dx.doi.org/10.1109/32.489081.

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5

Wang, Victoria, Kanak Agarwal, Sani R. Nassif, Kevin J. Nowka, and Dejan Markovic. "A Simplified Design Model for Random Process Variability." IEEE Transactions on Semiconductor Manufacturing 22, no. 1 (February 2009): 12–21. http://dx.doi.org/10.1109/tsm.2008.2011630.

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6

Fitzwater, LeRoy M., and Steven R. Winterstein. "Predicting Design Wind Turbine Loads from Limited Data: Comparing Random Process and Random Peak Models." Journal of Solar Energy Engineering 123, no. 4 (July 1, 2001): 364–71. http://dx.doi.org/10.1115/1.1409561.

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This paper considers two distinct topics that arise in reliability-based wind turbine design. First, it illustrates how general probability models can be used to predict long-term design loads from a set of limited-duration, short-term load histories. Second, it considers in detail the precise choice of probability model to be adopted, for both flap and edge bending loads in both parked and operating turbine conditions. In particular, a 3-moment random peak model and a 3- or 4-moment random process model are applied and compared. For a parked turbine, all models are found to be virtually unbiased and to notably reduce uncertainty in estimating extreme loads (e.g., by roughly 50%). For an operating turbine, however, only the random peak model is found to retain these beneficial features. This suggests the advantage of the random peak model, which appears to capture the rotating blade behavior sufficiently well to accurately predict extremes.

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7

KRIVELEVICH, MICHAEL, BENNY SUDAKOV, and DAN VILENCHIK. "On the Random Satisfiable Process." Combinatorics, Probability and Computing 18, no. 5 (September 2009): 775–801. http://dx.doi.org/10.1017/s0963548309990356.

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In this work we suggest a new model for generating random satisfiable k-CNF formulas. To generate such formulas. randomly permute all $2^k\binom{n}{k}$ possible clauses over the variables x1,. . .,xn, and starting from the empty formula, go over the clauses one by one, including each new clause as you go along if, after its addition, the formula remains satisfiable. We study the evolution of this process, namely the distribution over formulas obtained after scanning through the first m clauses (in the random permutation's order).Random processes with conditioning on a certain property being respected are widely studied in the context of graph properties. This study was pioneered by Ruciński and Wormald in 1992 for graphs with a fixed degree sequence, and also by Erdős, Suen and Winkler in 1995 for triangle-free and bipartite graphs. Since then many other graph properties have been studied, such as planarity and H-freeness. Thus our model is a natural extension of this approach to the satisfiability setting.Our main contribution is as follows. For m ≥ cn, c = c(k) a sufficiently large constant, we are able to characterize the structure of the solution space of a typical formula in this distribution. Specifically, we show that typically all satisfying assignments are essentially clustered in one cluster, and all but e−Ω(m/n)n of the variables take the same value in all satisfying assignments. We also describe a polynomial-time algorithm that finds w.h.p. a satisfying assignment for such formulas.

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8

Glushkov, A. N., M. Y. Kalinin, V. P. Litvinenko, and Y. V. Litvinenko. "Digital simulator of a random process using Markov model." Journal of Physics: Conference Series 1479 (March 2020): 012056. http://dx.doi.org/10.1088/1742-6596/1479/1/012056.

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9

Reimann, S. "Price dynamics from a simple multiplicative random process model." European Physical Journal B 56, no. 4 (April 2007): 381–94. http://dx.doi.org/10.1140/epjb/e2007-00141-4.

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10

RAWAL, S., and G. J. RODGERS. "MODELLING INFLATION AS A RANDOM PROCESS." International Journal of Theoretical and Applied Finance 06, no. 08 (December 2003): 821–27. http://dx.doi.org/10.1142/s0219024903002225.

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We introduce a model of inflation in which the prices of commodities are inflated by a random process. At each time step a price x is selected with a rate of xα and is inflated by a factor of 1/β where 0<β<1. For α=0, we obtain a general time-dependent solution, where the initial price distribution can be of any form. When α>0, in the long time limit, only the highest price inflates. For α<0, the model exhibits asymptotic scaling behavior. We also consider the effects of a time dependent β, where 0<β(t)<1, for the case α=0. We find that the price distribution approaches a steady state if β(t)-1~0 faster than 1/t.

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11

Dembélé, A., J. L. Bertrand-Krajewski, and B. Barillon. "Calibration of stormwater quality regression models: a random process?" Water Science and Technology 62, no. 4 (August 1, 2010): 875–82. http://dx.doi.org/10.2166/wst.2010.324.

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Regression models are among the most frequently used models to estimate pollutants event mean concentrations (EMC) in wet weather discharges in urban catchments. Two main questions dealing with the calibration of EMC regression models are investigated: i) the sensitivity of models to the size and the content of data sets used for their calibration, ii) the change of modelling results when models are re-calibrated when data sets grow and change with time when new experimental data are collected. Based on an experimental data set of 64 rain events monitored in a densely urbanised catchment, four TSS EMC regression models (two log-linear and two linear models) with two or three explanatory variables have been derived and analysed. Model calibration with the iterative re-weighted least squares method is less sensitive and leads to more robust results than the ordinary least squares method. Three calibration options have been investigated: two options accounting for the chronological order of the observations, one option using random samples of events from the whole available data set. Results obtained with the best performing non linear model clearly indicate that the model is highly sensitive to the size and the content of the data set used for its calibration.

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12

Richey, Jacob, and Amites Sarkar. "Intersections of random sets." Journal of Applied Probability 59, no. 1 (January 17, 2022): 131–51. http://dx.doi.org/10.1017/jpr.2021.34.

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AbstractWe consider a variant of a classical coverage process, the Boolean model in $\mathbb{R}^d$ . Previous efforts have focused on convergence of the unoccupied region containing the origin to a well-studied limit C. We study the intersection of sets centered at points of a Poisson point process confined to the unit ball. Using a coupling between the intersection model and the original Boolean model, we show that the scaled intersection converges weakly to the same limit C. Along the way, we present some tools for studying statistics of a class of intersection models.

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13

Lupenko, Sergiy, Nadiia Lutsyk, and Yuri Lapusta. "Cyclic Linear Random Process As A Mathematical Model Of Cyclic Signals." Acta Mechanica et Automatica 9, no. 4 (December 1, 2015): 219–24. http://dx.doi.org/10.1515/ama-2015-0035.

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Abstract In this study the cyclic linear random process is defined, that combines the properties of linear random process and cyclic random process. This expands the possibility describing cyclic signals and processes within the framework of linear random processes theory and generalizes their known mathematical model as a linear periodic random process. The conditions for the kernel are given and the probabilistic characteristics of generated process of linear random process in order to be a cyclic random process. The advantages of the cyclic linear random process are presented. It can be used as the mathematical model of the cyclic stochastic signals and processes in various fields of science and technology.

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14

Chen, Xiao Ming, Wen Qi Wu, and Song Song Li. "Random Yield Model in Integrated Circuit Design." Applied Mechanics and Materials 397-400 (September 2013): 1837–43. http://dx.doi.org/10.4028/www.scientific.net/amm.397-400.1837.

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As feature dimension of integrated circuits (IC) come into nanometer nodes, yield problems caused by random defects get worse. Even with advanced process techniques, the yield could not achieve 100%. Accurate prediction of yield can point out the direction of process optimization, shorten the production cycle, reduce the production cost, and then increase profits. In this paper, some kinds of random defects which can influence random yield are summarized. Then some widely used yield models are outlined and the drawbacks of these models are analyzed. At last, an improved yield model is proposed with the combination of Poisson model and negative binominal model. This model which takes distributions of random defects into consideration is more flexible and accurate. It can be seen from the simulation results that comparing to those existing models, the improved model indeed has higher fidelity and more flexibility.

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15

Quine, M. P., and J. Robinson. "A linear random growth model." Journal of Applied Probability 27, no. 3 (September 1990): 499–509. http://dx.doi.org/10.2307/3214536.

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Points start to form on an ‘uncovered' unit interval according to a Poisson process with parameter λ. From newly formed points a covering region grows in both directions at velocity v, while new points continue to form on uncovered parts of the interval. Eventually the whole interval will be covered. Let N ≧ 1 denote the total number of points formed. We derive integral expressions for E(N) and Var(N) and give precise asymptotic expressions for these moments as ρ = λ/v →∞. Asymptotic normality of N is also established.

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16

Quine, M. P., and J. Robinson. "A linear random growth model." Journal of Applied Probability 27, no. 03 (September 1990): 499–509. http://dx.doi.org/10.1017/s0021900200039061.

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Points start to form on an ‘uncovered' unit interval according to a Poisson process with parameter λ. From newly formed points a covering region grows in both directions at velocity v, while new points continue to form on uncovered parts of the interval. Eventually the whole interval will be covered. Let N ≧ 1 denote the total number of points formed. We derive integral expressions for E(N) and Var(N) and give precise asymptotic expressions for these moments as ρ = λ/v →∞. Asymptotic normality of N is also established.

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17

Schatzman, Evry. "Diffusion process produced by random internal waves." Journal of Fluid Mechanics 322 (September 10, 1996): 355–82. http://dx.doi.org/10.1017/s0022112096002820.

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The aim of the paper is to present a new transport process which is likely to have great importance for understanding the internal constitution of the stars.In order to set the problem in context, we first give a short presentation of the physical properties of the Sun and stars, described usually under the names Standard Solar Model or Standard Stellar Models (SSM). Next we show that an important shortcoming of SSM is that they do not explain the age dependence of the lithium deficiency of stars of known age: stars of galactic clusters and the Sun. It was suggested a long time ago that the presence of a macroscopic diffusion process in the radiative zone should be assumed, below the surface convective zone of solar-like stars. It is then possible for the lithium present in the convective zone to be carried to the thermonuclear burning level below the convective zone. The first assumption was that differential rotation generates turbulence and therefore that a turbulent diffusion process takes place. However, this model predicts a lithium abundance which is strongly rotation dependent, contrary to the observations. Furthermore, as the diffusion coefficient is large all over the radiative zone, it prevents the possibility of gravitational separation by diffusion and consequently leads to the impossibility of explaining the difference in helium abundance between the surface and the centre of the Sun. The consequence is obviously that we need to take into account another physical process.Stars having a mass M < 1.3M[odot ] have a convective zone which begins close to the stellar surface and extends down to a depth which is an appreciable fraction of the stellar radius. In the convective zone, strong stochastic motions carry, at least partially, heat transfer. These motions do not vanish at the lower boundary and generate internal waves into the radiative zone. These random internal waves are at the origin of a diffusion process which can be considered as responsible for the diffusive transport of lithium down to the lithium burning level. This is certainly not the only physical process responsible for lithium deficiency in main sequence stars, but its properties open the way to a completely consistent analysis of lithium deficiency.The model of generation of gravity waves is based on a model of heat transport in the convective zone by diving plumes. The horizontal component of the turbulent motion at the boundary of the convective zone is assumed to generate the horizontal motion of internal waves. The result is a large horizontal component of the diffusion coefficient, which produces in a short time an horizontally uniform chemical composition. It is known that gravity waves, in the absence of any dissipative process, cannot generate vertical mixing. Therefore, the vertical component of the diffusion coefficient is entirely dependent on radiative damping. It decreases quickly in the radiative zone, but is large enough to be responsible for lithium burning.Owing to the radial dependence of velocity amplitude, the diffusion coefficient increases when approaching the stellar centre. However, very close to the centre, nonlinear dissipative and radiative damping of internal waves become large and the diffusion coefficient vanishes at the very centre.

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18

Lu, Xuefei, Xiaoyan Wang, Yifang Yang, and Jianan Xue. "The Optimization Model for Reducing RON Loss in Gasoline Refining Process." Geofluids 2021 (February 19, 2021): 1–10. http://dx.doi.org/10.1155/2021/5520942.

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As gasoline is the main fuel of small vehicles, the exhaust emissions from its combustion will affect air quality. The focus of gasoline cleaning is to reduce the sulfur and olefin content in gasoline while maintaining its RON as much as possible. The reduction of RON will bring great economic losses to enterprises. Therefore, it is very important for petrochemical enterprises to construct a RON loss model in the gasoline refining process. The model construction, which reduces RON loss during gasoline refining, is the main question in this paper. By Python and SPSS software, we got two variable filtering methods: the random forest importance filtering and PCA filtering, and combined with SVR and random forest models, RON of the product and sulfur content were predicted. The filtering order of the original data by Excel and Python is maximum and minimum removal, 3σ criterion removal, deletion of too many sites in incomplete data, and filling of empty values in the mean within two hours. Several RON prediction models were established with the help of Python software, and the variables selected were compared by two filtering methods: one is the SVR model based on Gaussian, linear, polynomial, and Sigmoid kernel functions; the other is the random forest model. The sulfur content and RON prediction model was constructed, which use evaluation functions such as MSE, R 2 , and RMSE to evaluate and sulfur content as the subject condition. We convert the problem into linear and nonlinear model variable optimization problems: the linear model is the variable selected by the SVR linear kernel function model and random forest; the nonlinear model is the combination of variables selected by the random forest model and random forest. Optimizing for each sample, the optimization method is to find the optimal solution for each variable and use the optimal method for each variable as the local optimal solution for the sample. The two models are evaluated from the perspectives of optimization degree, optimization rate, model running speed, etc.

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19

Xie, Huan, Wei Zeng, Hong Song, Wen Sun, and Tao Ren. "A Novel Combination Co-Kriging Model Based on Gaussian Random Process." Mathematical Problems in Engineering 2018 (September 3, 2018): 1–10. http://dx.doi.org/10.1155/2018/6372572.

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Co-Kriging (CK) modeling provides an efficient way to predict responses of complicated engineering problems based on a set of sample data obtained by methods with varying degree of accuracy and computation cost. In this work, the Gaussian random process (GRP) is introduced to construct a novel combination CK model (CK-GRP) to improve the prediction accuracy of the conventional CK model, in which all the sample information provided by different correlation models is well utilized. The features of the new model are demonstrated and evaluated for a numerical case and an engineering application. It is shown that the CK-GRP model proposed in this work is effective and can be used to improve the prediction accuracy and robustness of the CK model.

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20

Dragan, Yaroslav P., and G. M. Osukhivskaya. "Description of Sound Cardiosignals by Periodically Correlated Random Process Model." Journal of Automation and Information Sciences 31, no. 7-9 (1999): 59–63. http://dx.doi.org/10.1615/jautomatinfscien.v31.i7-9.100.

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21

Keller, Peter, Sylvie Rœlly, and Angelo Valleriani. "A Quasi Random Walk to Model a Biological Transport Process." Methodology and Computing in Applied Probability 17, no. 1 (September 20, 2013): 125–37. http://dx.doi.org/10.1007/s11009-013-9372-5.

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22

Xi, Yunping, and Zdeněk P. Bazǎnt. "Random growth of crack with R-curve: Markov process model." Engineering Fracture Mechanics 57, no. 6 (August 1997): 593–608. http://dx.doi.org/10.1016/s0013-7944(97)00069-6.

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23

Ciavarella, Michele, and Antonio Papangelo. "A random process asperity model for adhesion between rough surfaces." Journal of Adhesion Science and Technology 31, no. 22 (March 18, 2017): 2445–67. http://dx.doi.org/10.1080/01694243.2017.1304856.

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24

Pecháček, T., R. W. Goosmann, V. Karas, B. Czerny, and M. Dovčiak. "Hot-spot model for accretion disc variability as random process." Astronomy & Astrophysics 556 (July 31, 2013): A77. http://dx.doi.org/10.1051/0004-6361/201220339.

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25

Pecháček, T., V. Karas, and B. Czerny. "Hot-spot model for accretion disc variability as random process." Astronomy & Astrophysics 487, no. 3 (July 9, 2008): 815–30. http://dx.doi.org/10.1051/0004-6361:200809720.

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26

CAI, JINHAI, and ZHI-QIANG LIU. "MARKOV PROCESS IN PATTERN RECOGNITION." International Journal of Image and Graphics 01, no. 02 (April 2001): 287–311. http://dx.doi.org/10.1142/s0219467801000189.

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Using the Markov random process, we developed two new approaches to pattern recognition: (1) Hidden Markov model for modeling spectral features for recognizing 2D shapes. This is because Fourier spectra are suitable for describing 2D shapes of simple closed contours and probabilistic models are capable of coping with random variations in object shapes. We will analyze the properties of spectral features derived from contours of 2D shapes and use these features in 2D pattern recognition. (2) Markov random fields for modeling 2D structural and statistical features. We will give a theoretic analysis of this approach, discuss the issues in the design of neighborhood system and cliques for Markov random field models, and analyze the properties of the models. We have applied the proposed approach to the recognition of unconstrained handwritten numerals and 2D shapes. Our extensive experimental results show that the proposed approach can achieve a higher performance than that reported recently in the literature.

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27

Yan, Yu Tao, Zhi Li Sun, Guang Wei Hu, and Li Fang Liu. "Wear Reliability Analysis Method Based on Random Process." Applied Mechanics and Materials 155-156 (February 2012): 348–51. http://dx.doi.org/10.4028/www.scientific.net/amm.155-156.348.

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The random reliability analysis model for wear was established based on random process theory and wear research. The wear experiment scheme on load, sliding speed, surface hardness and bearing capacity of lubrication was instituted by the uniform design method, and carried out on a vertical universal friction/wear tester. The static wear predication model was established by the partial least squares based on test data. It is found that the wear extent obey to normal distribution by checkout of the probability paper and mathematic expectation function fitting and residuals distribution, the variance function fitting and residuals distribution based on the test data of random process. The reliability of definite working life was gained by calculating with established reliability model, and compared with test data, the analysis method is a valid method for wear reliability.

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28

Sun, Zhi Li, Yun Feng Zhang, and Yu Tao Yan. "Experimental Research on Wear Random Process." Advanced Materials Research 126-128 (August 2010): 976–80. http://dx.doi.org/10.4028/www.scientific.net/amr.126-128.976.

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The wear volume is obtained by means of experiment and the wear random process model is established according to the result. The Carbon steel material is used and the samples are grouped five after surface treatment, each group tests six times under the same condition. The wear volume under each wear time shows big dispersion. The additional study indicates that the sample has the large wear volume is in the serious wear state from the beginning, and the wear of running-in phase is inflected by the work velocity and the state condition of the surface of the samples. The wear process which the mean value is a constant and the standard deviation is different is a normal process generally, it is a stationary normal process if the standard deviation has no relation to the start of the wear time, or a Wiener process if the standard deviation is liner with the wear time, it is valuable to forecast the wear reliability.

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29

Daley, D. J., and J. Gani. "A random allocation model for carrier-borne epidemics." Journal of Applied Probability 30, no. 4 (December 1993): 751–65. http://dx.doi.org/10.2307/3214510.

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A carrier-borne epidemic is considered in which the carriers, subject to a death process, infect susceptibles by random allocation rather than the classical homogeneous mixing process. An explicit solution for the probability generating function (p.g.f.) of the process is obtained, and a probabilistic analysis of carrier models provided. The sizes and durations of the random allocation and classical carrier epidemics are compared. The strongest comparisons concern sample path results based on the probabilistic analysis; this also gives a sounder basis for computational work.

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30

Daley, D. J., and J. Gani. "A random allocation model for carrier-borne epidemics." Journal of Applied Probability 30, no. 04 (December 1993): 751–65. http://dx.doi.org/10.1017/s0021900200044545.

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A carrier-borne epidemic is considered in which the carriers, subject to a death process, infect susceptibles by random allocation rather than the classical homogeneous mixing process. An explicit solution for the probability generating function (p.g.f.) of the process is obtained, and a probabilistic analysis of carrier models provided. The sizes and durations of the random allocation and classical carrier epidemics are compared. The strongest comparisons concern sample path results based on the probabilistic analysis; this also gives a sounder basis for computational work.

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31

Avlasenko, Ilona, Lyudmila Avlasenko, Isa Peshkhoev, Yuri Podkolzin, and Oksana Savelyeva. "Enterprise growth simulation model." E3S Web of Conferences 175 (2020): 12006. http://dx.doi.org/10.1051/e3sconf/202017512006.

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Simulation mathematical model of small enterprise functioning is under analysis in this article. It is assumed that annual working capital profitability and loan rate are random variables with normal distribution, the amount of borrowed capital does not exceed the amount of own working capital. Given the value of its working capital at the beginning of time, its dependence on time is constructed as a random process. The parameters of random variables are estimated based on the processing of statistical data on the previous activities of this enterprise. The implementation of the random process is statistically modeled. With the help of the statistical tests, implementations of random function of growth of own working capital are built and the probability of bankruptcy is estimated as relative frequency of cases of adoption of negative value by random function. It is proposed to use the built simulation model of the enterprise to estimate the probability of bankruptcy of the studied enterprise in the coming period (a given number ofyears).

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32

Sun, Li, Xiaohui Gu, and Pu Song. "Accelerated Degradation Process Analysis Based on the Nonlinear Wiener Process with Covariates and Random Effects." Mathematical Problems in Engineering 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/5246108.

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It is assumed that the drift parameter is dependent on the acceleration variables and the diffusion coefficient remains the same across the whole accelerated degradation test (ADT) in most of the literature based on Wiener process. However, the diffusion coefficient variation would also become obvious in some applications with the stress increasing. Aiming at the phenomenon, the paper concludes that both the drift parameter and the diffusion parameter depend on stress variables based on the invariance principle of failure mechanism and Nelson assumption. Accordingly, constant stress accelerated degradation process (CSADP) and step stress accelerated degradation process (SSADP) with random effects are modeled. The unknown parameters in the established model are estimated based on the property of degradation and degradation increment, separately for CASDT and SSADT, by the maximum likelihood estimation approach with measurement error. In addition, the simulation steps of accelerated degradation data are provided and simulated step stress accelerated degradation data is designed to validate the proposed model compared to other models. Finally, a case study of CSADT is conducted to demonstrate the benefits of our model in the practical engineering.

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33

Tang, Shengjin, Xiaosong Guo, Chuanqiang Yu, Haijian Xue, and Zhijie Zhou. "Accelerated Degradation Tests Modeling Based on the Nonlinear Wiener Process with Random Effects." Mathematical Problems in Engineering 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/560726.

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Accelerated degradation tests (ADT) modeling is an important issue in lifetime assessment to the products with high reliability and long lifetime. Among the literature about the accelerated nonlinear degradation process modeling, the current methods did not consider the product-to-product variation of the products with the same type. Therefore, this paper proposes an accelerated degradation process modeling method with random effects for the nonlinear Wiener process. Firstly, we derive the lifetime distribution of the nonlinear Wiener process with random effects. Secondly, the nonlinear Wiener process is used to model the degradation process of a single stress, and the drift coefficient is considered as a random variable to describe the product-to-product variation. Using the random acceleration model, the random effects are incorporated into the constant stress ADT models and the step stress ADT models. Then, a two-step maximum likelihood estimation (MLE) method is presented to estimate the unknown parameters in the degradation models. Finally, a simulation study and a case study are provided to demonstrate the application and superiority of the proposed model.

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34

Xiang, Dao, and Wen-Hui Huang. "Investigations on collective behavior in radiation process with random walk model." Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 240, no. 4 (December 2005): 855–62. http://dx.doi.org/10.1016/j.nimb.2005.06.198.

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35

Turchyn, Ievgen. "A multiplicative wavelet-based model for simulation of a random process." Modern Stochastics: Theory and Applications 2, no. 4 (September 23, 2015): 309–25. http://dx.doi.org/10.15559/15-vmsta33.

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36

Welsh, D. J. A. "Percolation in the random cluster process and Q-state Potts model." Journal of Physics A: Mathematical and General 26, no. 11 (June 7, 1993): 2471–83. http://dx.doi.org/10.1088/0305-4470/26/11/002.

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37

Chen, Hao, Tianbiao Yu, Jinlong Dong, Yu Zhao, and Ji Zhao. "Kinematic simulation of surface grinding process with random cBN grain model." International Journal of Advanced Manufacturing Technology 100, no. 9-12 (October 20, 2018): 2725–39. http://dx.doi.org/10.1007/s00170-018-2840-x.

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38

Volf, P. "A random point process model for the score in sport matches." IMA Journal of Management Mathematics 20, no. 2 (August 29, 2008): 121–31. http://dx.doi.org/10.1093/imaman/dpn027.

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39

Lee, N. H., and C. E. Priebe. "A latent process model for time series of attributed random graphs." Statistical Inference for Stochastic Processes 14, no. 3 (June 30, 2011): 231–53. http://dx.doi.org/10.1007/s11203-011-9058-y.

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40

Prajneshu and R. Venugopalan. "von Bertalanffy growth model in a random environment." Canadian Journal of Fisheries and Aquatic Sciences 56, no. 6 (June 1, 1999): 1026–30. http://dx.doi.org/10.1139/f99-035.

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The well-known von Bertalanffy growth model for describing age-length relationship is formulated in a randomly fluctuating environment. The fluctuations in the system are assumed to be described by a Gaussian white noise stochastic process. The resulting model, in terms of a stochastic differential equation, is solved analytically. It is shown that the probability density function of length of a fish is a Gaussian stochastic process. Finally, as an illustration, the methodology is applied to a set of pearl oyster (Pinctada fucata (Gould)) data.

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41

Papangelou, F. "A Simple Model for Random Oscillations." Journal of Applied Probability 47, no. 04 (December 2010): 1164–73. http://dx.doi.org/10.1017/s0021900200007440.

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A simple model for a randomly oscillating variable is suggested, which is a variant of the two-state random velocity model. As in the latter model, the variable keeps rising or falling with constant velocity for some time before randomly reversing its direction. In contrast however, its propensity to reverse depends on its current value and it is for this desirable feature that the model is proposed here. This feature has two implications: (a) neither the changing variable nor its velocity is Markovian, although the joint process is, and (b) the linear differential equations arising in the case of our model do not have constant coefficients. The results given in this paper are meant to illustrate the straightforward nature of some of the calculations involved and to highlight the relationship with one-dimensional diffusions.

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Papangelou, F. "A Simple Model for Random Oscillations." Journal of Applied Probability 47, no. 4 (December 2010): 1164–73. http://dx.doi.org/10.1239/jap/1294170527.

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Abstract:

A simple model for a randomly oscillating variable is suggested, which is a variant of the two-state random velocity model. As in the latter model, the variable keeps rising or falling with constant velocity for some time before randomly reversing its direction. In contrast however, its propensity to reverse depends on its current value and it is for this desirable feature that the model is proposed here. This feature has two implications: (a) neither the changing variable nor its velocity is Markovian, although the joint process is, and (b) the linear differential equations arising in the case of our model do not have constant coefficients. The results given in this paper are meant to illustrate the straightforward nature of some of the calculations involved and to highlight the relationship with one-dimensional diffusions.

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43

Ahlberg, Daniel, and Johan Tykesson. "Gilbert's disc model with geostatistical marking." Advances in Applied Probability 50, no. 4 (November 29, 2018): 1075–94. http://dx.doi.org/10.1017/apr.2018.51.

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AbstractWe study a variant of Gilbert's disc model, in which discs are positioned at the points of a Poisson process in ℝ2with radii determined by an underlying stationary and ergodic random field φ:ℝ2→[0,∞), independent of the Poisson process. This setting, in which the random field is independent of the point process, is often referred to asgeostatistical marking. We examine how typical properties of interest in stochastic geometry and percolation theory, such as coverage probabilities and the existence of long-range connections, differ between Gilbert's model with radii given by some random field and Gilbert's model with radii assigned independently, but with the same marginal distribution. Among our main observations we find that complete coverage of ℝ2does not necessarily happen simultaneously, and that the spatial dependence induced by the random field may both increase as well as decrease the critical threshold for percolation.

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Brown, Mark, Erol A. Peköz, and Sheldon M. Ross. "A Random Permutation Model Arising in Chemistry." Journal of Applied Probability 45, no. 04 (December 2008): 1060–70. http://dx.doi.org/10.1017/s0021900200004976.

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We study a model arising in chemistry where n elements numbered 1, 2, …, n are randomly permuted and if i is immediately to the left of i + 1 then they become stuck together to form a cluster. The resulting clusters are then numbered and considered as elements, and this process keeps repeating until only a single cluster is remaining. In this article we study properties of the distribution of the number of permutations required.

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45

Brown, Mark, Erol A. Peköz, and Sheldon M. Ross. "A Random Permutation Model Arising in Chemistry." Journal of Applied Probability 45, no. 4 (December 2008): 1060–70. http://dx.doi.org/10.1239/jap/1231340233.

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We study a model arising in chemistry where n elements numbered 1, 2, …, n are randomly permuted and if i is immediately to the left of i + 1 then they become stuck together to form a cluster. The resulting clusters are then numbered and considered as elements, and this process keeps repeating until only a single cluster is remaining. In this article we study properties of the distribution of the number of permutations required.

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46

Suo, Shaoyi, Linsong Jiang, Ping Wang, and Maozhao Xie. "Study of the porous media random structure model." Modern Physics Letters B 34, no. 10 (January 31, 2020): 2050090. http://dx.doi.org/10.1142/s0217984920500906.

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The random structure model of porous media is constructed by the gravity packed method, which can give a random packed structure that is similar to the actual packed bed structure by simulating the free fall, collision and stacking process of pellets via the OpenFOAM. Different from the existing ordered structure model of porous media, the structure model adopted in this paper has strong randomness since it simulates the actual generation process of the porous media material. Meanwhile, the following batch modeling instructions are completed with the MATLAB, which can ensure that the random structure model of porous media has the advantages of high similarity with the actual porous structure and rapid modeling.

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47

Lapsa, P. M. "Determination of Gegenbauer-type random process models." Signal Processing 63, no. 1 (November 1997): 73–90. http://dx.doi.org/10.1016/s0165-1684(97)00142-4.

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48

Giraitis, Liudas, Remigijus Leipus, and Donatas Surgailis. "AGGREGATION OF THE RANDOM COEFFICIENT GLARCH(1,1) PROCESS." Econometric Theory 26, no. 2 (September 30, 2009): 406–25. http://dx.doi.org/10.1017/s026646660910004x.

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The paper discusses contemporaneous aggregation of the Linear ARCH (LARCH) model as defined in (1), which was introduced in Robinson (1991) and studied in Giraitis, Robinson, and Surgailis (2000) and other works. We show that the limiting aggregate of the (G)eneralized LARCH(1,1) process in (3)–(4) with random Beta distributed coefficient β exhibits long memory. In particular, we prove that squares of the limiting aggregated process have slowly decaying correlations and their partial sums converge to a self-similar process of a new type.

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Navarro-Quiles, A., J. V. Romero, M. D. Roselló, and M. A. Sohaly. "Approximating the Solution Stochastic Process of the Random Cauchy One-Dimensional Heat Model." Abstract and Applied Analysis 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/5391368.

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This paper deals with the numerical solution of the random Cauchy one-dimensional heat model. We propose a random finite difference numerical scheme to construct numerical approximations to the solution stochastic process. We establish sufficient conditions in order to guarantee the consistency and stability of the proposed random numerical scheme. The theoretical results are illustrated by means of an example where reliable approximations of the mean and standard deviation to the solution stochastic process are given.

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Meng, Na, Jian Zhong Zhang, Bao Qing Dai, and Xin Li Chen. "Point Cloud Process of Laser Scanning with a Mathematical Noise Model." Applied Mechanics and Materials 275-277 (January 2013): 2537–42. http://dx.doi.org/10.4028/www.scientific.net/amm.275-277.2537.

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Considering the unreasonable noise of laser scanning point data during measuring, which causes the reconstructed curve and surface rough, some problems are analyzed to deal with noise. The mathematical noise model on scanning point cloud is proposed, which consists of deterministic and random noise error, and the random error mainly consists of geometric error and measurement one. The data process is proposed to reduce noise and to simplify data. The noise process consists of obvious noise removed, random filter algorithm and data fairing with an optimized correction value. Due to redundant data about mass point cloud, method of combining deviation parameters with allowed angle is proposed to simplify point cloud. The experiments show that the proposed method has many obvious advantages than a single algorithm of data processing, such as all sorts of noise data can be removed respectively, mass data can be streamlined. And the proposed algorithm has the advantages of high reservation of curve and surface reconstruction of point cloud.

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