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Journal articles on the topic 'Differential probability'

Author: Grafiati

Published: 30 May 2022

Last updated: 31 May 2022

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1

SMOLYANOV, O. G., and H. v. WEIZSÄCKER. "SMOOTH PROBABILITY MEASURES AND ASSOCIATED DIFFERENTIAL OPERATORS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 02, no. 01 (March 1999): 51–78. http://dx.doi.org/10.1142/s0219025799000047.

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We compare different notions of differentiability of a measure along a vector field on a locally convex space. We consider in the L2-space of a differentiable measure the analog of the classical concepts of gradient, divergence and Laplacian (which coincides with the Ornstein–Uhlenbeck operator in the Gaussian case). We use these operators for the extension of the basic results of Malliavin and Stroock on the smoothness of finite dimensional image measures under certain nonsmooth mappings to the case of non-Gaussian measures. The proof of this extension is quite straight forward and does not use any Chaos-decomposition. Finally, the role of this Laplacian in the procedure of quantization of anharmonic oscillators is discussed.

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2

Barchielli, A., A. M. Paganoni, and F. Zucca. "On stochastic differential equations and semigroups of probability operators in quantum probability." Stochastic Processes and their Applications 73, no. 1 (January 1998): 69–86. http://dx.doi.org/10.1016/s0304-4149(97)00093-8.

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3

Zhou, Shizhong, and Shiyi Lan. "The Intersection Probability of Brownian Motion and SLEκ." Advances in Mathematical Physics 2015 (2015): 1–5. http://dx.doi.org/10.1155/2015/627423.

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By using excursion measure Poisson kernel method, we obtain a second-order differential equation of the intersection probability of Brownian motion andSLEκ. Moreover, we find a transformation such that the second-order differential equation transforms into a hypergeometric differential equation. Then, by solving the hypergeometric differential equation, we obtain the explicit formula of the intersection probability for the trace of the chordalSLEκand planar Brownian motion started from distinct points in an upper half-planeH-.

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4

Watson, Jane M. "Building probability models in a differential equations course." International Journal of Mathematical Education in Science and Technology 22, no. 4 (July 1991): 507–17. http://dx.doi.org/10.1080/0020739910220402.

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5

Myung, I. J., V. Balasubramanian, and M. A. Pitt. "Counting probability distributions: Differential geometry and model selection." Proceedings of the National Academy of Sciences 97, no. 21 (September 26, 2000): 11170–75. http://dx.doi.org/10.1073/pnas.170283897.

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6

Lefebvre, Mario. "Similarity Solutions of Partial Differential Equations in Probability." Journal of Probability and Statistics 2011 (2011): 1–13. http://dx.doi.org/10.1155/2011/689427.

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Two-dimensional diffusion processes are considered between concentric circles and in angular sectors. The aim of the paper is to compute the probability that the process will hit a given part of the boundary of the stopping region first. The appropriate partial differential equations are solved explicitly by using the method of similarity solutions and the method of separation of variables. Some solutions are expressed as generalized Fourier series.

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7

Ruzhentsev, Victor. "The conditions of provable security of block ciphers against truncated differential attack." Studia Scientiarum Mathematicarum Hungarica 52, no. 2 (June 2015): 176–84. http://dx.doi.org/10.1556/012.2015.52.2.1307.

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The modified method of estimation of the resistance of block ciphers to truncated byte differential attack is proposed. The previously known method estimate the truncated byte differential probability for Rijndael-like ciphers. In this paper we spread the sphere of application of that method on wider class of ciphers. The proposed method based on searching the most probable truncated byte differential characteristics and verification of sufficient conditions of effective byte differentials absence.

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8

Wu, Yong, and Xiang Hu. "Ruin Probability in Compound Poisson Process with Investment." Journal of Applied Mathematics 2012 (2012): 1–7. http://dx.doi.org/10.1155/2012/286792.

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We consider that the surplus of an insurer follows compound Poisson process and the insurer would invest its surplus in risky assets, whose prices satisfy the Black-Scholes model. In the risk process, we decompose the ruin probability into the sum of two ruin probabilities which are caused by the claim and the oscillation, respectively. We derive the integro-differential equations for these ruin probabilities these ruin probabilities. When the claim sizes are exponentially distributed, third-order differential equations of the ruin probabilities are derived from the integro-differential equations and a lower bound is obtained.

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9

Kohlmann, M. "Stochastic differential equation." Metrika 33, no. 1 (December 1986): 246. http://dx.doi.org/10.1007/bf01894752.

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10

Dong, Jinshuo, Aaron Roth, and Weijie J. Su. "Gaussian differential privacy." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 84, no. 1 (February 2022): 3–37. http://dx.doi.org/10.1111/rssb.12454.

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11

Okagbue, Hilary I., Muminu O. Adamu, and Timothy A. Anake. "Ordinary differential equations of probability functions of convoluted distributions." International Journal of ADVANCED AND APPLIED SCIENCES 5, no. 10 (October 2018): 46–52. http://dx.doi.org/10.21833/ijaas.2018.10.007.

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12

Lai, Shih-Kung, and Jhong-You Huang. "Differential effects of outcome and probability on risky decision." Applied Economics Letters 26, no. 21 (April 16, 2019): 1790–97. http://dx.doi.org/10.1080/13504851.2019.1602699.

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13

Gander, Walter. "From Elementary Probability to Stochastic Differential Equations With MAPLE." Journal of the American Statistical Association 98, no. 461 (March 2003): 254–55. http://dx.doi.org/10.1198/jasa.2003.s260.

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14

Wang, Yuye, Jing Yang, and Jianpei Zhang. "Differential Privacy for Weighted Network Based on Probability Model." IEEE Access 8 (2020): 80792–800. http://dx.doi.org/10.1109/access.2020.2991062.

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15

Ignatyev, Oleksiy. "Partial asymptotic stability in probability of stochastic differential equations." Statistics & Probability Letters 79, no. 5 (March 2009): 597–601. http://dx.doi.org/10.1016/j.spl.2008.10.005.

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16

Diem, Ho Kieu, Vo Duy Trung, Nguyen Thoi Trung, Vo Van Tai, and Nguyen Trang Thao. "A Differential Evolution-Based Clustering for Probability Density Functions." IEEE Access 6 (2018): 41325–36. http://dx.doi.org/10.1109/access.2018.2849688.

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17

Schober, R., Yao Ma, and S. Pasupathy. "On the error probability of decision-feedback differential detection." IEEE Transactions on Communications 51, no. 4 (April 2003): 535–38. http://dx.doi.org/10.1109/tcomm.2003.810857.

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18

Kim, Sangtae, Jaewon Kim, Dong-Joon Shin, Dae-Ig Chang, and Wonjin Sung. "Error probability expressions for frame synchronization using differential correlation." Journal of Communications and Networks 12, no. 6 (December 2010): 582–91. http://dx.doi.org/10.1109/jcn.2010.6388305.

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19

CARDALIAGUET, P., and M. QUINCAMPOIX. "DETERMINISTIC DIFFERENTIAL GAMES UNDER PROBABILITY KNOWLEDGE OF INITIAL CONDITION." International Game Theory Review 10, no. 01 (March 2008): 1–16. http://dx.doi.org/10.1142/s021919890800173x.

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We study a zero-sum differential game where the players have only an unperfect information on the state of the system. In the beginning of the game only a random distribution on the initial state is available. The main result of the paper is the existence of the value obtained through an uniqueness result for Hamilton-Jacobi-Isaacs equations stated on the space of measure in ℝn. This result is the first step for future work on differential games with lack of information.

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20

Xu, Zixiang, Ahmet Unveren, and Adnan Acan. "Probability collectives hybridised with differential evolution for global optimisation." International Journal of Bio-Inspired Computation 8, no. 3 (2016): 133. http://dx.doi.org/10.1504/ijbic.2016.076652.

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21

Selçuk, Ali Aydın. "On Probability of Success in Linear and Differential Cryptanalysis." Journal of Cryptology 21, no. 1 (September 14, 2007): 131–47. http://dx.doi.org/10.1007/s00145-007-9013-7.

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22

Teslenko, V. I. "Fourth-Order Differential Equation for a Two-Stage Absorbing Markov Chain with a Stochastic Forward Transition Probability." Ukrainian Journal of Physics 62, no. 4 (May 2017): 349–61. http://dx.doi.org/10.15407/ujpe62.04.0349.

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23

Kurz, Christoph. "Understanding differential privacy." Significance 18, no. 3 (May 26, 2021): 24–27. http://dx.doi.org/10.1111/1740-9713.01528.

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24

Buckdahn, Rainer, and Shige Peng. "Stationary backward stochastic differential equations and associated partial differential equations." Probability Theory and Related Fields 115, no. 3 (1999): 383. http://dx.doi.org/10.1007/s004400050242.

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25

Belenky, Vadim L. "A Capsizing Probability Computation Method." Journal of Ship Research 37, no. 03 (September 1, 1993): 200–207. http://dx.doi.org/10.5957/jsr.1993.37.3.200.

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A new method of computing capsizing probability is described. This method is based on a partially linear approximation of nonlinear terms in the rolling differential equation. This substitution permits the retention of the topology of the nonlinear phase portrait and, at the same time, the simplicity of the linear solution. A criterion of stability of a system with partially linear righting moments is suggested. Finally, a practical method of computer-aided calculation of capsizing probability is described.

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26

Lestari, Andriani Adi, and Nunik Yulianingsih. "Distribusi Difference dari S-Box Berbasis Fungsi Balikan Pada GF(28)." Jurnal Matematika 6, no. 2 (December 30, 2016): 93. http://dx.doi.org/10.24843/jmat.2016.v06.i02.p72.

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Substitution-box (s-box) is a basic component of block cipher which performs a substitution. Two powerful cryptanalysis techniques applied to block ciphers are linear cryptanalysis and differential cryptanalysis. The resistance against differential cryptanalysis can be achieved by eliminating high-probability differential trails. We should choose an s-box where the maximum difference propagation probability is as small as possible to eliminating high-probability differential trails. Nyberg proposed a method to construct the s-box by using the inverse mapping on a finite field then implements affine transformations on . In this study, we generate 47.104 s-box according to Nyberg. The experimental results showed that s-boxes have the maximum difference propagation probability with the same frequency.

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27

JUMARIE, GUY. "ON SOME SIMILARITIES AND DIFFERENCES BETWEEN FRACTIONAL PROBABILITY DENSITY SIGNED MEASURE OF PROBABILITY AND QUANTUM PROBABILITY." Modern Physics Letters B 23, no. 06 (March 10, 2009): 791–805. http://dx.doi.org/10.1142/s0217984909019041.

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A probability density of fractional (or fractal) order is defined by the probability increment pr{x < X ≤ x+dx} = pα(x)(dx)α, 0 < α < 1, and appears to be quite suitable to deal with random variables defined in a fractal space. Combining this definition with the fractional Taylor's series [Formula: see text] denotes the Mittag–Leffler function) provided by the modified Riemann–Liouville derivative, one can expand a probability calculus parallel to the standard one. This approach could be considered as a framework for the derivation of some space fractional partial differential diffusion equations in coarse-grained spaces. It is shown firstly that there is some relation between fractional probability and signed measure of probability, and secondly that when α = 1/2, there is some identity between this fractal probability and quantum probability. Shortly, a wavefunction could be thought of as a fractal probability density of order 1/2. One exhibits further relations with possibility theory and relative information. Lastly, one arrives at a new informational entropy based on the inverse of the Mittag–Leffler function.

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28

Mahdaviani, Mahshid, Javidan Kazemi Kordestani, Alireza Rezvanian, and Mohammad Reza Meybodi. "LADE: Learning Automata Based Differential Evolution." International Journal on Artificial Intelligence Tools 24, no. 06 (December 2015): 1550023. http://dx.doi.org/10.1142/s0218213015500232.

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Many engineering optimization problems do not standard mathematical techniques, and cannot be solved using exact algorithms. Evolutionary algorithms have been successfully used for solving such optimization problems. Differential evolution is a simple and efficient population-based evolutionary algorithm for global optimization, which has been applied in many real world engineering applications. However, the performance of this algorithm is sensitive to appropriate choice of its parameters as well as its mutation strategy. In this paper, we propose two different underlying classes of learning automata based differential evolution for adaptive selection of crossover probability and mutation strategy in differential evolution. In the first class, genomes of the population use the same mutation strategy and crossover probability. In the second class, each genome of the population adjusts its own mutation strategy and crossover probability parameter separately. The performance of the proposed methods is analyzed on ten benchmark functions from CEC 2005 and one real-life optimization problem. The obtained results show the efficiency of the proposed algorithms for solving real-parameter function optimization problems.

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29

Park, Peter Y., Luis F. Miranda-Moreno, and Frank F. Saccomanno. "Estimation of speed differentials on rural highways using hierarchical linear regression models." Canadian Journal of Civil Engineering 37, no. 4 (April 2010): 624–37. http://dx.doi.org/10.1139/l10-002.

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Large speed differentials between highway segments are associated with an increase in the number of accidents. Traditional speed differential measures, derived from single-level linear regression models, suffer from serious deficiencies, namely underestimating the speed differential (due to intracorrelated data) and inflating the adequacy of the model’s explanation (due to aggregate data). High-quality speed differential predictions are highly desirable right from the initial design phase, but the estimation process is not straightforward, and decision makers must recognize that speed differential predictions are subject to considerable uncertainty. This paper compares four models: two single-level models, a conventional multilevel model, and a Bayes multilevel model. The results show empirically that multilevel models increase the accuracy and precision of estimates of speed differentials, possibly with fewer data. The paper introduces a new, easy to interpret speed consistency measure that simply represents the probability that a vehicle exceeds a certain speed differential. This measure is calculated using a multilevel model and takes into account the uncertainty in the estimates of speed differentials. Overall, we show that a multilevel modeling approach can improve the quality of decision making that makes use of speed differential information in road design and road safety.

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30

Fa, Kwok Sau. "Integro-differential Schrödinger equation and description of unstable particle." Modern Physics Letters B 28, no. 30 (December 10, 2014): 1450234. http://dx.doi.org/10.1142/s0217984914502340.

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The description of a particle in the quantum system is probabilistic. In the ordinary quantum mechanics the total probability of finding the particle is conserved, i.e. the probability is normalized for all the times. To find a non-constant total probability an imaginary term should be added to the potential energy which is not physical. Recently, generalizations of the ordinary Schrödinger equation have been proposed by using the Feynman path integral and analogy between the Schrödinger equation and diffusion equation. In this work, an integro-differential Schrödinger equation is proposed by using analogy between the Schrödinger equation and diffusion equation. The equation is obtained from the continuous time random walk model with diverging jump length variance and generic waiting time probability density. The equation generalizes the ordinary and fractional Schrödinger equations. One can show that the integro-differential Schrödinger equation can describe a non-constant total probability for a free particle, and it includes the exponential decay which is fundamental for the description of radioactive decay.

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31

Boullion, Thomas L., John W. Seaman, and Dean M. Young. "Moments of Discrete Probability Distributions Derived Using a Differential Operator." American Statistician 46, no. 1 (February 1992): 22. http://dx.doi.org/10.2307/2684404.

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32

Prèmont, G., P. Lalanne, P. Chavel, M. Kuijk, and P. Heremans. "Generation of sigmoid probability functions by clipped differential speckle detection." Optics Communications 129, no. 5-6 (September 1996): 347–52. http://dx.doi.org/10.1016/s0030-4018(96)00163-0.

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33

Boullion, Thomas L., John W. Seaman, and Dean M. Young. "Moments of Discrete Probability Distributions Derived Using a Differential Operator." American Statistician 46, no. 1 (February 1992): 22–24. http://dx.doi.org/10.1080/00031305.1992.10475840.

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34

Liu, Jingsen, Li Liu, and Yu Li. "A Differential Evolution Flower Pollination Algorithm with Dynamic Switch Probability." Chinese Journal of Electronics 28, no. 4 (July 1, 2019): 737–47. http://dx.doi.org/10.1049/cje.2019.04.008.

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35

Lu, Wen, Yong Ren, and Lanying Hu. "Mean-field backward stochastic differential equations in general probability spaces." Applied Mathematics and Computation 263 (July 2015): 1–11. http://dx.doi.org/10.1016/j.amc.2015.04.014.

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36

PREMONT, G., P. LALANNE, P. CHAVEL, M. KUIJK, and P. HEREMANS. "Generation of sigmoid probability functions by clipped differential speckle detection." Optics Communications 129, no. 5-6 (September 1, 1996): 347–52. http://dx.doi.org/10.1016/0030-4018(96)00163-0.

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37

Nie, Weilin, and Cheng Wang. "Probability comprehension of differential privacy for privacy protection algorithms: A new measure." International Journal of Wavelets, Multiresolution and Information Processing 15, no. 04 (April 17, 2017): 1750033. http://dx.doi.org/10.1142/s0219691317500333.

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Differential privacy becomes a standard for evaluating the privacy protection performance for an algorithm these years. However, the definition of differential privacy seems not so easy to understand as the classical k-anonymity and etc. In this paper, we propose a new measure which is more comprehensible. Some properties of such measure are investigated and the relationship between our new definition and differential privacy is studied.

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38

Wong, Eugene, and Moshe Zakai. "Multiparameter martingale differential forms." Probability Theory and Related Fields 74, no. 3 (September 1987): 429–53. http://dx.doi.org/10.1007/bf00699099.

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39

Luo, Shangzhen. "A stochastic differential game for quadratic-linear diffusion processes." Advances in Applied Probability 48, no. 4 (December 2016): 1161–82. http://dx.doi.org/10.1017/apr.2016.69.

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AbstractIn this paper we study a stochastic differential game between two insurers whose surplus processes are modelled by quadratic-linear diffusion processes. We consider an exit probability game. One insurer controls its risk process to minimize the probability that the surplus difference reaches a low level (indicating a disadvantaged surplus position of the insurer) before reaching a high level, while the other insurer aims to maximize the probability. We solve the game by finding the value function and the Nash equilibrium strategy in explicit forms.

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40

Møller, Christian Max. "Stochastic differential equations for ruin probabilities." Journal of Applied Probability 32, no. 1 (March 1995): 74–89. http://dx.doi.org/10.2307/3214922.

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The present paper proposes a general approach for finding differential equations to evaluate probabilities of ruin in finite and infinite time. Attention is given to real-valued non-diffusion processes where a Markov structure is obtainable. Ruin is allowed to occur upon a jump or between the jumps. The key point is to define a process of conditional ruin probabilities and identify this process stopped at the time of ruin as a martingale. Using the theory of marked point processes together with the change-of-variable formula or the martingale representation theorem for point processes, we obtain differential equations for evaluating the probability of ruin.Numerical illustrations are given by solving a partial differential equation numerically to obtain the probability of ruin over a finite time horizon.

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41

Møller, Christian Max. "Stochastic differential equations for ruin probabilities." Journal of Applied Probability 32, no. 01 (March 1995): 74–89. http://dx.doi.org/10.1017/s002190020010258x.

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The present paper proposes a general approach for finding differential equations to evaluate probabilities of ruin in finite and infinite time. Attention is given to real-valued non-diffusion processes where a Markov structure is obtainable. Ruin is allowed to occur upon a jump or between the jumps. The key point is to define a process of conditional ruin probabilities and identify this process stopped at the time of ruin as a martingale. Using the theory of marked point processes together with the change-of-variable formula or the martingale representation theorem for point processes, we obtain differential equations for evaluating the probability of ruin. Numerical illustrations are given by solving a partial differential equation numerically to obtain the probability of ruin over a finite time horizon.

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42

Babak, Vitaly, Volodymyr Kharchenko, and Volodymyr Vasylyev. "USING GENERALIZED STOCHASTIC METHOD TO EVALUATE PROBABILITY OF CONFLICT IN CONTROLLED AIR TRAFFIC." Aviation 11, no. 2 (March 31, 2007): 31–36. http://dx.doi.org/10.3846/16487788.2007.9635958.

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The introduction of the new concepts of air traffic management (ATM) and transition from centralized to decentralized air traffic control (ATC) with the change of traditional ATM to Cooperative ATM sets new tasks and opens new capabilities for air traffic safety systems. This paper is devoted to the problem of evaluating the probability of aircraft collision under the condition of Cooperative ATM, when the necessary information is available to the subjects involved in the decision‐making process. The generalized stochastic conflict probability evaluation method is developed. This method is based on the generalized conflict probability equation for evaluation of potential conflict probability and aircraft collision probability that is derived by taking into account stochastic nature and time correlation of deviation from planned flight trajectory in controlled air traffic. This equation is described as a multi‐dimensional parabolic partial differential equation using a differential (infinitesimal) operator of the multi‐dimensional stochastic process of relative aircraft movement. The common procedure for the prediction of conflict probability is given, and the practical application of the generalized method presented is shown. All equational coefficients of a differential operator for a practical solution of a parabolic partial differential equation are derived. For some conditions, the numerical solution of the conflict probability equation is obtained and illustrated graphically.

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43

Bracken. "Exterior Differential Systems for Higher Order Partial Differential Equations." Journal of Mathematics and Statistics 6, no. 1 (January 1, 2010): 52–55. http://dx.doi.org/10.3844/jmssp.2010.52.55.

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44

Zacks, Shelemyahu, and Thomas C. Gard. "Introduction to Stochastic Differential Equations." Journal of the American Statistical Association 84, no. 408 (December 1989): 1104. http://dx.doi.org/10.2307/2290110.

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45

Peng, Shige, and Zhe Yang. "Anticipated backward stochastic differential equations." Annals of Probability 37, no. 3 (May 2009): 877–902. http://dx.doi.org/10.1214/08-aop423.

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46

Martin, Jaime San. "One-Dimensional Stratonovich Differential Equations." Annals of Probability 21, no. 1 (January 1993): 509–53. http://dx.doi.org/10.1214/aop/1176989414.

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47

Dynkin, E. B. "Superprocesses and Partial Differential Equations." Annals of Probability 21, no. 3 (July 1993): 1185–262. http://dx.doi.org/10.1214/aop/1176989116.

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48

Norin, N. V. "Stochastic Integrals and Differential Measures." Theory of Probability & Its Applications 32, no. 1 (January 1988): 107–16. http://dx.doi.org/10.1137/1132010.

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49

Ahmad, R., and T. C. Gard. "Introduction to Stochastic Differential Equations." Applied Statistics 37, no. 3 (1988): 446. http://dx.doi.org/10.2307/2347318.

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50

Wang, Gang. "Differential Subordination and Strong Differential Subordination for Continuous-Time Martingales and Related Sharp Inequalities." Annals of Probability 23, no. 2 (April 1995): 522–51. http://dx.doi.org/10.1214/aop/1176988278.

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