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Journal articles on the topic 'Stochastic modelling'

To see the other types of publications on this topic, follow the link: Stochastic modelling.

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Published: 4 June 2021

Last updated: 28 July 2024

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1

Varetsky, Y., and Z. Hanzelka. "STOCHASTIC MODELLING OF A HYBRID RENEWABLE ENERGY SYSTEM." Tekhnichna Elektrodynamika 2016, no. 2 (March 10, 2016): 58–62. http://dx.doi.org/10.15407/techned2016.02.058.

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2

Dobrow, Robert P. "Applied Stochastic Modelling." Technometrics 44, no. 1 (February 2002): 91. http://dx.doi.org/10.1198/tech.2002.s667.

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3

Albert, Jim. "Applied Stochastic Modelling." Journal of the American Statistical Association 97, no. 457 (March 2002): 354–55. http://dx.doi.org/10.1198/jasa.2002.s448.

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4

Auton, Tim. "Applied Stochastic Modelling." Journal of the Royal Statistical Society: Series D (The Statistician) 52, no. 2 (July 2003): 244. http://dx.doi.org/10.1111/1467-9884.t01-2-00356.

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5

Hartley, R., M. H. A. Davies, and R. B. Vintner. "Stochastic Modelling and Control." Journal of the Operational Research Society 37, no. 9 (September 1986): 928. http://dx.doi.org/10.2307/2582813.

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6

Blokker, Mirjam. "Stochastic Water Demand Modelling." Water Intelligence Online 10 (2011): 9781780400853. http://dx.doi.org/10.2166/9781780400853.

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7

Stemler, Thomas, Johannes P. Werner, Hartmut Benner, and Wolfram Just. "Stochastic modelling of intermittency." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1910 (January 13, 2010): 273–84. http://dx.doi.org/10.1098/rsta.2009.0196.

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Recently, methods have been developed to model low-dimensional chaotic systems in terms of stochastic differential equations. We tested such methods in an electronic circuit experiment. We aimed to obtain reliable drift and diffusion coefficients even without a pronounced time-scale separation of the chaotic dynamics. By comparing the analytical solutions of the corresponding Fokker–Planck equation with experimental data, we show here that crisis-induced intermittency can be described in terms of a stochastic model which is dominated by state-space-dependent diffusion. Further on, we demonstrate and discuss some limits of these modelling approaches using numerical simulations. This enables us to state a criterion that can be used to decide whether a stochastic model will capture the essential features of a given time series.

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8

Hartley, R. "Stochastic Modelling and Control." Journal of the Operational Research Society 37, no. 9 (November 1986): 928–29. http://dx.doi.org/10.1057/jors.1986.158.

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9

Jones, P. W. "Stochastic Modelling and Analysis." Technometrics 30, no. 3 (August 1988): 361. http://dx.doi.org/10.1080/00401706.1988.10488425.

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10

Cui, Lirong, and Haitao Liao. "Stochastic modelling with applications." IMA Journal of Management Mathematics 32, no. 1 (September 7, 2020): 1–2. http://dx.doi.org/10.1093/imaman/dpaa018.

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11

Cairns, Andrew J. G., and Gary Parker. "Stochastic pension fund modelling." Insurance: Mathematics and Economics 21, no. 1 (October 1997): 43–79. http://dx.doi.org/10.1016/s0167-6687(97)00018-8.

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12

Daunizeau, J., S. Kiebel, and K. Friston. "Stochastic Dynamic Causal Modelling." NeuroImage 47 (July 2009): S147. http://dx.doi.org/10.1016/s1053-8119(09)71500-9.

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13

Manzoni, Stefano, Annalisa Molini, and Amilcare Porporato. "Stochastic modelling of phytoremediation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, no. 2135 (June 22, 2011): 3188–205. http://dx.doi.org/10.1098/rspa.2011.0209.

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Leaching of heavy metals and other contaminants from soils poses a significant environmental threat as it affects the quality of downstream water bodies. Quantifying these losses is particularly important when employing phytoremediation approaches to reduce soil contamination, as contaminant escaping the system through leaching cannot be taken up by vegetation. Despite its undoubted importance, the role of such hydrologic forcing has seldom been fully considered in models describing the long-term contaminant mass balance during phytoremediation. The partitioning of contaminants between leaching and vegetation uptake is controlled by a number of biophysical processes as well as rainfall variability. Here, we develop a novel stochastic framework that provides analytical expressions to quantify the partitioning of contaminants between leaching and plant uptake and the probability of phytoremediation duration as a function of rainfall statistics and soil and vegetation characteristics. Simple expressions for the mean phytoremediation duration and effectiveness (defined as the fraction of contaminant that is recovered in plant biomass) are derived. The proposed framework can be employed to estimate under which conditions phytoremediation is more efficient, as well as to design phytoremediation projects that maximize contaminant recovery and minimize the duration of the remediation process.

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14

Ferschl, Franz. "Stochastic modelling and analysis." European Journal of Operational Research 28, no. 1 (January 1987): 113–14. http://dx.doi.org/10.1016/0377-2217(87)90185-8.

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15

Zuidweg, J. K. "Stochastic modelling and control." European Journal of Operational Research 29, no. 3 (June 1987): 391. http://dx.doi.org/10.1016/0377-2217(87)90259-1.

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16

Guzman, L., Y. Chen, S. Potter, W. Zhong, and M. Rahman. "Application of stochastic modelling for simulating hemp fibre peeling behaviour." Canadian Biosystems Engineering 55, no. 1 (December 19, 2013): 2.1–2.8. http://dx.doi.org/10.7451/cbe.2013.55.2.1.

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17

Vanita Jha, Raj Vir Singh, and S R Bhakar. "Stochastic Modelling of Soil Moisture." Journal of Agricultural Engineering (India) 40, no. 4 (December 31, 2003): 51–56. http://dx.doi.org/10.52151/jae2003404.1056.

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The study was conducted to develop a stochastic model for the soil moisture data of 19 years (1980-1998) for an average depth of 3D-em. The soil moisture series was assumed to be composed of periodic and stochastic component as the trend component was found to be insignificant. The autoregressive stochastic model was fitted to the soil moisture data. By statistical analysis the closeness between generated and historical series was observed. The developed model was then validated by generating data for the last 3 years (1999 -2001) and compared it with observed data for the same years. Mean and standard deviation of the model was found to be very close to observed data, which proves the validity of model.

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18

TĂNASE, DOBRE, OANA CRISTINA PÂRVULESCU, and CRISTIAN RĂDUCANU. "Stochastic modelling of polysaccharide hydrolysis." Journal of Engineering Sciences and Innovation 3, no. 1 (January 10, 2018): 25–38. http://dx.doi.org/10.56958/jesi.2018.3.1.25.

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A stochastic model was selected and developed to describe polysaccharide hydrolysis kinetics. This model can accurately predict the hydrolysis kinetics and covers the limitations of some classical kinetic models (e.g., complexity of mathematical models, large number of parameter estimations, change in parameters with a change in hydrolysis conditions, etc.). One of the main advantages of the stochastic mathematical model approach is represented by the fact that the polysaccharide structural characteristics and operating parameters can be separately incorporated into the model. The stochastic process characterizing the model considers that the breakdown of a polysaccharide by hydrolysis is a random process based on the cleavage of a parent macromolecule within a molecular mass range into two descendants within lower molecular mass ranges. The model description and its implementation in the hydrolysis of a hypothetical polysaccharide were presented.

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19

Callan, Torrington, and Stephen Woodcock. "Stochastic modelling of chlamydial infections." ANZIAM Journal 61 (July 6, 2020): C89—C103. http://dx.doi.org/10.21914/anziamj.v61i0.15159.

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Chlamydia trachomatis is a bacterial pathogen that can cause serious reproductive harm. We describe a class of stochastic branching processes and their application in modelling the growth of an infection by Chlamydia. Using simulations we show that the model can reproduce biological phenomena of interest, and we show the variability in outcomes of infections under the same parameter conditions. We further speculate how this model might be used to explain long-term adverse reproductive sequelae. References Y. M. AbdelRahman and R. J. Belland. The chlamydial developmental cycle. FEMS Microbio. Rev., 29(5):949–959, 2005. doi:10.1016/j.femsre.2005.03.002. T. E. Harris. Branching processes. Ann. Math. Stat., 19(4):474–494, 12 1948. doi:10.1214/aoms/1177730146. C. Jacob. Branching processes: Their role in epidemiology. Int. J. Env. Res. Public Health, 7(3):1186–1204, 2019. doi:10.3390/ijerph7031204. N. Low, M. Egger, J. A. C. Sterne, R. M. Harbord, F. Ibrahim, B. Lindblom, and B. Herrmann. Incidence of severe reproductive tract complications associated with diagnosed genital chlamydial infection: The Uppsala women's cohort study. Sexually Trans. Infect., 82(3):212–218, 2006. doi:10.1136/sti.2005.017186. D. Mallet, M. Bagher-Oskouei, A. Farr, D. Simpson, and K. Sutton. A mathematical model of chlamydial infection incorporating movement of chlamydial particles. Bull. Math. Bio., 75:2257–2270, 10 2013. doi:10.1007/s11538-013-9891-9. H. K. Maxion, W. Liu, M.-H. Chang, and K. A. Kelly. The infecting dose of chlamydia muridarum modulates the innate immune response and ascending infection. Infect. Immun., 72(11):6330–6340, 2004. doi:10.1128/IAI.72.11.6330-6340.2004. S. Menon, P. Timms, J. A. Allan, K. Alexander, L. Rombauts, P. Horner, M. Keltz, J. Hocking, and W. M. Huston. Human and pathogen factors associated with chlamydia trachomatis-related infertility in women. Clinic. Microbio. Rev., 28(4):969–985, 2015. doi:10.1128/CMR.00035-15. D. P. Wilson. Mathematical modelling of chlamydia. In J. Crawford and A. J. Roberts, editors, Proc. of 11th Computational Techniques and Applications Conference CTAC-2003, ANZIAM J., volume 45, pages C201–C214, 2004. doi:10.21914/anziamj.v45i0.883. D. P. Wilson and D. L. S. McElwain. A model of neutralization of chlamydia trachomatis based on antibody and host cell aggregation on the elementary body surface. J. Theor. Bio., 226(3):321–330, 2004. doi:10.1016/j.jtbi.2003.09.010. D. P. Wilson, P. Timms, and D. L. S. McElwain. A mathematical model for the investigation of the Th1 immune response to chlamydia trachomatis. Math. Biosci., 182(1):27–44, 2003. doi:10.1016/S0025-5564(02)00180-3.

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20

He, Y., Mahmut Horasan, P. Taylor, and G. Ramsay. "Stochastic Modelling For Risk Assessment." Fire Safety Science 7 (2003): 333–44. http://dx.doi.org/10.3801/iafss.fss.7-333.

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21

B. S. DEORA and R. V. SINGH. "Stochastic modelling of water deficit." Journal of Agrometeorology 11, no. 1 (June 1, 2009): 19–28. http://dx.doi.org/10.54386/jam.v11i1.1217.

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A stochastic model for weekly water deficit series, using 28 years climatological data, under climatic condition of S.K. Nagar has been developed. The turning point test and Kendall’s rank correlation test are applied for detecting the trend. Correlogram technique is used to detect the periodicity, which is then analyzed by Fourier series method. Significant harmonics were also identified. The statistical properties of the generated water deficit series were compared with observed series. The developed model was validated by predicting two years ahead and compared with the observed water deficit series, The test results indicated the high degree of model fitness. The developed model may be used for representing the time-based structure of the water deficit time series.

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22

Schoenberg, Ronald, Andreas Diekmann, and Peter Mitter. "Stochastic Modelling of Social Processes." Contemporary Sociology 15, no. 3 (May 1986): 449. http://dx.doi.org/10.2307/2070077.

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23

Pettere, Gaida. "Stochastic modelling of insurance liabilities." Acta et Commentationes Universitatis Tartuensis de Mathematica 13 (December 31, 2009): 25–35. http://dx.doi.org/10.12697/acutm.2009.13.03.

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Our aim is to present a method for estimating incurred but not reported (IBNR) claim reserves. Each claim is described by threecharacteristics: the claim size, the allocated loss adjusted expense and the development time. We concentrate on the joint study of all three random variables. First, the marginal univariate distributions are estimated using families of lognormal, Pareto, Wald and Gamma distributions. Next, the matrix of dependence characteristics is found between the three variables and then different multivariate copulas are used to model the joint distribution. The obtained models are fitted to the real data of motor liability insurance of a Latvian insurance company. By simulation the average claim size and allocated loss adjustment expenses in each development day have been estimated. Finally, outstanding claim reserve has been estimated.

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24

Wang, Joanna J. J., S. T. Boris Choy, and Jennifer S. K. Chan. "Modelling stochastic volatility using generalizedtdistribution." Journal of Statistical Computation and Simulation 83, no. 2 (February 2013): 340–54. http://dx.doi.org/10.1080/00949655.2011.608067.

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25

ARINGA, HENRY P., CHRISTOPHER C. BERNIDO, M. VICTORIA CARPIO-BERNIDO, and JINKY B. BORNALES. "STOCHASTIC MODELLING OF HELICAL BIOPOLYMERS." International Journal of Modern Physics: Conference Series 17 (January 2012): 73–76. http://dx.doi.org/10.1142/s2010194512007957.

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We model helical polypeptides in an aqueous environment by explicitly evaluating winding probabilities of biopolymers. To account for differences in reaction to the solvent of the various types of amino acids forming the chainlike biopolymer, a length-dependent drift coefficient A(s) is used. As an application, we express A(s) in terms of a Bessel function to generate a sequence of winding and non-winding segments and compare this with the α-helical segments of myoglobin.

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26

Krupp, A. U., I. M. Griffiths, and C. P. Please. "Stochastic modelling of membrane filtration." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2200 (April 2017): 20160948. http://dx.doi.org/10.1098/rspa.2016.0948.

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Membrane fouling during particle filtration occurs through a variety of mechanisms, including internal pore clogging by contaminants, coverage of pore entrances and deposition on the membrane surface. In this paper, we present an efficient method for modelling the behaviour of a filter, which accounts for different retention mechanisms, particle sizes and membrane geometries. The membrane is assumed to be composed of a series of, possibly interconnected, pores. The central feature is a conductivity function , which describes the blockage of each individual pore as particles arrive, which is coupled with a mechanism to account for the stochastic nature of the arrival times of particles at the pore. The result is a system of ordinary differential equations based on the pore-level interactions. We demonstrate how our model can accurately describe a wide range of filtration scenarios. Specifically, we consider a case where blocking via multiple mechanisms can occur simultaneously, which have previously required the study through individual models; the filtration of a combination of small and large particles by a track-etched membrane and particle separation using interconnected pore networks. The model is significantly faster than comparable stochastic simulations for small networks, enabling its use as a tool for efficient future simulations.

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27

Ellam, L., M. Girolami, G. A. Pavliotis, and A. Wilson. "Stochastic modelling of urban structure." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2213 (May 2018): 20170700. http://dx.doi.org/10.1098/rspa.2017.0700.

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The building of mathematical and computer models of cities has a long history. The core elements are models of flows (spatial interaction) and the dynamics of structural evolution. In this article, we develop a stochastic model of urban structure to formally account for uncertainty arising from less predictable events. Standard practice has been to calibrate the spatial interaction models independently and to explore the dynamics through simulation. We present two significant results that will be transformative for both elements. First, we represent the structural variables through a single potential function and develop stochastic differential equations to model the evolution. Second, we show that the parameters of the spatial interaction model can be estimated from the structure alone, independently of flow data, using the Bayesian inferential framework. The posterior distribution is doubly intractable and poses significant computational challenges that we overcome using Markov chain Monte Carlo methods. We demonstrate our methodology with a case study on the London, UK, retail system.

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28

Burrell, Quentin L. "Book Review: Applied stochastic modelling." Statistical Methods in Medical Research 11, no. 5 (October 2002): 451–52. http://dx.doi.org/10.1177/096228020201100511.

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29

Hemerly, Elder M. "MEMS IMU stochastic error modelling." Systems Science & Control Engineering 5, no. 1 (December 7, 2016): 1–8. http://dx.doi.org/10.1080/21642583.2016.1262801.

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30

Smouse, Peter E., Stefano Focardi, Paul R. Moorcroft, John G. Kie, James D. Forester, and Juan M. Morales. "Stochastic modelling of animal movement." Philosophical Transactions of the Royal Society B: Biological Sciences 365, no. 1550 (July 27, 2010): 2201–11. http://dx.doi.org/10.1098/rstb.2010.0078.

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Modern animal movement modelling derives from two traditions. Lagrangian models, based on random walk behaviour, are useful for multi-step trajectories of single animals. Continuous Eulerian models describe expected behaviour, averaged over stochastic realizations, and are usefully applied to ensembles of individuals. We illustrate three modern research arenas. (i) Models of home-range formation describe the process of an animal ‘settling down’, accomplished by including one or more focal points that attract the animal's movements. (ii) Memory-based models are used to predict how accumulated experience translates into biased movement choices, employing reinforced random walk behaviour, with previous visitation increasing or decreasing the probability of repetition. (iii) Lévy movement involves a step-length distribution that is over-dispersed, relative to standard probability distributions, and adaptive in exploring new environments or searching for rare targets. Each of these modelling arenas implies more detail in the movement pattern than general models of movement can accommodate, but realistic empiric evaluation of their predictions requires dense locational data, both in time and space, only available with modern GPS telemetry.

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31

López-Rubio, Ezequiel, and Rafael Marcos Luque-Baena. "Stochastic approximation for background modelling." Computer Vision and Image Understanding 115, no. 6 (June 2011): 735–49. http://dx.doi.org/10.1016/j.cviu.2011.01.007.

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32

Pesmazoglou, I., A. M. Kempf, and S. Navarro-Martinez. "Stochastic modelling of particle aggregation." International Journal of Multiphase Flow 80 (April 2016): 118–30. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2015.12.004.

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33

Menezes, Raquel, and A. Manuela Gonçalves. "Spatio-temporal stochastic modelling (METMAVI)." Stochastic Environmental Research and Risk Assessment 28, no. 5 (February 28, 2014): 1167–69. http://dx.doi.org/10.1007/s00477-014-0860-0.

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34

Bonzani, I., and L. Mussone. "Stochastic modelling of traffic flow." Mathematical and Computer Modelling 36, no. 1-2 (July 2002): 109–19. http://dx.doi.org/10.1016/s0895-7177(02)00107-3.

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35

Crowder, Martin, H. M. Taylor, and S. Karlin. "An Introduction to Stochastic Modelling." Statistician 44, no. 2 (1995): 291. http://dx.doi.org/10.2307/2348464.

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36

Thomas, P., and S. Haykin. "Stochastic modelling of radar returns." IEE Proceedings F Communications, Radar and Signal Processing 133, no. 5 (1986): 476. http://dx.doi.org/10.1049/ip-f-1.1986.0075.

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37

Reznicek, K., and T. C. E. Cheng. "Stochastic modelling of reservoir operations." European Journal of Operational Research 50, no. 3 (February 1991): 235–48. http://dx.doi.org/10.1016/0377-2217(91)90257-v.

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38

Reynolds, David, and Jagannathan Gomatam. "Stochastic modelling of Genetic Algorithms." Artificial Intelligence 82, no. 1-2 (April 1996): 303–30. http://dx.doi.org/10.1016/0004-3702(94)00091-3.

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39

Fennell, D. A., A. Pallaska, M. Corbo, and F. E. Cotter. "Stochastic modelling of apoptosis kinetics." Apoptosis 10, no. 2 (March 2005): 447–52. http://dx.doi.org/10.1007/s10495-005-0818-2.

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40

Schmidt, K. D. "Stochastic modelling in experience rating." Insurance: Mathematics and Economics 13, no. 2 (November 1993): 158. http://dx.doi.org/10.1016/0167-6687(93)90894-u.

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41

Al-Begain, Khalid, Dieter Fiems, and Jean-Marc Vincent. "Analytical and stochastic modelling techniques." Annals of Operations Research 239, no. 2 (April 2016): 355–57. http://dx.doi.org/10.1007/s10479-016-2168-6.

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42

Amparore, Elvio G. "Stochastic modelling and evaluation using GreatSPN." ACM SIGMETRICS Performance Evaluation Review 49, no. 4 (June 2, 2022): 87–91. http://dx.doi.org/10.1145/3543146.3543165.

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GreatSPN is a tool that supports model-based (stochastic) analysis of Discrete Event Dynamic Systems (DEDS) modeled as Generalized Stochastic Petri Nets or one of its extensions like StochasticWell-formed Nets, Deterministic and Stochastic Petri Nets among the other. Performance evaluation of the timed and stochastic properties of the modeled systems was the initial reason for the tool development, and it is today a large and flexible framework that incorporates several analysis techniques, performance index types, variegated transition timing specifications, etc. In this paper we report the current status of the GreatSPN framework, with a focus on the modularity, the types of stochastic analysis, the specification and evaluation functionalities, and its role for the performance evaluation.

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43

Shymanska, Alla V., and Vitali A. Babakov. "Fast Monte Carlo Method in Stochastic Modelling of Charged Particle Multiplication." International Journal of Applied Physics and Mathematics 5, no. 3 (2015): 218–26. http://dx.doi.org/10.17706/ijapm.2015.5.3.218-226.

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44

Majda, Andrew J., Christian Franzke, and Boualem Khouider. "An applied mathematics perspective on stochastic modelling for climate." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1875 (April 29, 2008): 2427–53. http://dx.doi.org/10.1098/rsta.2008.0012.

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Systematic strategies from applied mathematics for stochastic modelling in climate are reviewed here. One of the topics discussed is the stochastic modelling of mid-latitude low-frequency variability through a few teleconnection patterns, including the central role and physical mechanisms responsible for multiplicative noise. A new low-dimensional stochastic model is developed here, which mimics key features of atmospheric general circulation models, to test the fidelity of stochastic mode reduction procedures. The second topic discussed here is the systematic design of stochastic lattice models to capture irregular and highly intermittent features that are not resolved by a deterministic parametrization. A recent applied mathematics design principle for stochastic column modelling with intermittency is illustrated in an idealized setting for deep tropical convection; the practical effect of this stochastic model in both slowing down convectively coupled waves and increasing their fluctuations is presented here.

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45

Van Rooy, Dirk. "Stochastic Modelling of a Contaminated Aquifer." Hydrology Research 17, no. 4-5 (August 1, 1986): 315–24. http://dx.doi.org/10.2166/nh.1986.0023.

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A stochastic solute transport model is applied to a groundwater contamination case. The contamination is caused by leachate from an unprotected landfill situated in a highly-permeable unconfined aquifer. The stochastic model combines the geostatistical techniques of semivariogram analysis and kriging with a numerical solute transport model. A Monte Carlo approach that utilizes the turning bands technique to genereate transmissivity fields is used. Here some preliminary results of the unconditional stochastic simulations are presented. The contaminant plume is characterized by expected concentrations of chloride and standard deviations.

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46

Frederiksen, Jorgen S., Terence J. O'Kane, and Meelis J. Zidikheri. "Subgrid modelling for geophysical flows." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1982 (January 13, 2013): 20120166. http://dx.doi.org/10.1098/rsta.2012.0166.

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Recently developed closure-based and stochastic model approaches to subgrid-scale modelling of eddy interactions are reviewed. It is shown how statistical dynamical closure models can be used to self-consistently calculate the eddy damping and stochastic backscatter parameters, required in large eddy simulations (LESs), from higher resolution simulations. A closely related direct stochastic modelling scheme that is more generally applicable to complex models is then described and applied to LESs of quasi-geostrophic turbulence of the atmosphere and oceans. The fundamental differences between atmospheric and oceanic LESs, which are related to the difference in the deformation scales in the two classes of flows, are discussed. It is noted that a stochastic approach may be crucial when baroclinic instability is inadequately resolved. Finally, inhomogeneous closure theory is applied to the complex problem of flow over topography; it is shown that it can be used to understand the successes and limitations of currently used heuristic schemes and to provide a basis for further developments in the future.

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47

Herzog, Bodo. "Fractional Stochastic Search Algorithms: Modelling Complex Systems via AI." Mathematics 11, no. 9 (April 26, 2023): 2061. http://dx.doi.org/10.3390/math11092061.

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The aim of this article is to establish a stochastic search algorithm for neural networks based on the fractional stochastic processes {BtH,t≥0} with the Hurst parameter H∈(0,1). We define and discuss the properties of fractional stochastic processes, {BtH,t≥0}, which generalize a standard Brownian motion. Fractional stochastic processes capture useful yet different properties in order to simulate real-world phenomena. This approach provides new insights to stochastic gradient descent (SGD) algorithms in machine learning. We exhibit convergence properties for fractional stochastic processes.

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48

Hamam, Haneen, Ali Raza, Manal M. Alqarni, Jan Awrejcewicz, Muhammad Rafiq, Nauman Ahmed, Emad E. Mahmoud, Witold Pawłowski, and Muhammad Mohsin. "Stochastic Modelling of Lassa Fever Epidemic Disease." Mathematics 10, no. 16 (August 13, 2022): 2919. http://dx.doi.org/10.3390/math10162919.

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Evolutionary approaches have a critical role in different disciplines such as real-world problems, computer programming, machine learning, biological sciences, and many more. The design of the stochastic model is based on transition probabilities and non-parametric techniques. Positivity, boundedness, and equilibria are investigated in deterministic and stochastic senses. An essential tool, Euler–Maruyama, is studied for the solution of said model. Standard and nonstandard evolutionary approaches are presented for the stochastic model in terms of efficiency and low-cost approximations. The standard evolutionary procedures like stochastic Euler–Maruyama and stochastic Runge–Kutta fail to restore the essential features of biological problems. On the other hand, the proposed method is efficient, of meager cost, and adopts all the desired feasible properties. At the end of this paper the comparison section is presented to support efficient analysis.

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Andrzejczak, Karol. "Stochastic Modelling Of The Repairable System." Journal of KONBiN 35, no. 1 (November 1, 2015): 5–14. http://dx.doi.org/10.1515/jok-2015-0034.

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Abstract All reliability models consisting of random time factors form stochastic processes. In this paper we recall the definitions of the most common point processes which are used for modelling of repairable systems. Particularly this paper presents stochastic processes as examples of reliability systems for the support of the maintenance related decisions. We consider the simplest one-unit system with a negligible repair or replacement time, i.e., the unit is operating and is repaired or replaced at failure, where the time required for repair and replacement is negligible. When the repair or replacement is completed, the unit becomes as good as new and resumes operation. The stochastic modelling of recoverable systems constitutes an excellent method of supporting maintenance related decision-making processes and enables their more rational use.

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Carkovs, Jevgeņijs, and Oksana Pavlenko. "Stochastic Modelling for Dynamics of Interacting Populations." Proceedings of the Latvian Academy of Sciences. Section B. Natural, Exact, and Applied Sciences. 73, no. 5 (October 1, 2019): 455–61. http://dx.doi.org/10.2478/prolas-2019-0070.

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Abstract The paper deals with a mathematical model for two interacting populations. Under the assumption of fast stochastic contacting of populations, we derive stochastic Poisson-type differential equations with a small parameter and propose an approximative algorithm for quantitative analysis of population dynamics that consists of two steps. First, we derive an ordinary differential equation for mean value of each population growth and analyse the average asymptotic population behaviour. Then, applying diffusion approximation procedure, we derive a stochastic Ito differential equation for small random deviations on the average motion in a form of a linear non-homogeneous Ito stochastic differential equation and analyse the probabilistic characteristics of the Gaussian process given by this equation.

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