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Journal articles on the topic 'Stochastic differential equations'

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Published: 4 June 2021
Last updated: 9 June 2025

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1

Norris, J. R., and B. Oksendal. "Stochastic Differential Equations." Mathematical Gazette 77, no. 480 (November 1993): 393. http://dx.doi.org/10.2307/3619809.

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2

Syed Tahir Hussainy and Pathmanaban K. "A study on analytical solutions for stochastic differential equations via martingale processes." Journal of Computational Mathematica 6, no. 2 (December 7, 2022): 85–92. http://dx.doi.org/10.26524/cm151.

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In this paper, we propose some analytical solutions of stochastic differential equations related to Martingale processes. In the first resolution, the answers of some stochastic differential equations are connected to other stochastic equations just with diffusion part (or drift free). The second suitable method is to convert stochastic differential equations into ordinary ones that it is tried to omit diffusion part of stochastic equation by applying Martingale processes. Finally, solution focuses on change of variable method that can be utilized about stochastic differential equations which are as function of Martingale processes like Wiener process, exponential Martingale process and differentiable processes.
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3

BOUFOUSSI, B., and N. MRHARDY. "MULTIVALUED STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS VIA BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS." Stochastics and Dynamics 08, no. 02 (June 2008): 271–94. http://dx.doi.org/10.1142/s0219493708002317.

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In this paper, we establish by means of Yosida approximation, the existence and uniqueness of the solution of a backward doubly stochastic differential equation whose coefficient contains the subdifferential of a convex function. We will use this result to prove the existence of stochastic viscosity solution for some multivalued parabolic stochastic partial differential equation.
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4

Tunc, Cemil, and Zozan Oktan. "STABILITY AND BOUNDEDNESS OF STOCHASTIC INTEGRO-DELAY DIFFERENTIAL EQUATIONS." Journal of Mathematical Analysis 15, no. 5 (October 30, 2024): 69–83. https://doi.org/10.54379/jma-2024-5-5.

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This work addresses stochastic integro-delay differential equations (SIDDEs) of second order with two constant delays. In the study, two new results including sufficient conditions on stochastic asymptotic stability and stochastic boundedness in probability of solutions of the given SIDDEs are proved. The proofs of new results are done by using a Lyapunov-Krasovskii functional (L-KF) as a basic tool. To demonstrate the validity of the obtained results, two examples are provided. According to a comparison with previous literature, the results of this study are new and also allow new contributions to the qualitative theory of SIDDEs.
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5

MTW and H. Kunita. "Stochastic Flows and Stochastic Differential Equations." Journal of the American Statistical Association 93, no. 443 (September 1998): 1251. http://dx.doi.org/10.2307/2669903.

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6

Krylov, Nicolai. "Stochastic flows and stochastic differential equations." Stochastics and Stochastic Reports 51, no. 1-2 (November 1994): 155–58. http://dx.doi.org/10.1080/17442509408833949.

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7

Jacka, S. D., and H. Kunita. "Stochastic Flows and Stochastic Differential Equations." Journal of the Royal Statistical Society. Series A (Statistics in Society) 155, no. 1 (1992): 175. http://dx.doi.org/10.2307/2982680.

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8

Halanay, A., T. Morozan, and C. Tudor. "Bounded solutions of affine stochastic differential equations and stability." Časopis pro pěstování matematiky 111, no. 2 (1986): 127–36. http://dx.doi.org/10.21136/cpm.1986.118271.

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9

Tleubergenov, Marat, and Gulmira Ibraeva. "ON THE CLOSURE OF STOCHASTIC DIFFERENTIAL EQUATIONS OF MOTION." Eurasian Mathematical Journal 12, no. 2 (2021): 82–89. http://dx.doi.org/10.32523/2077-9879-2021-12-2-82-89.

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10

Eliazar, Iddo. "Selfsimilar stochastic differential equations." Europhysics Letters 136, no. 4 (November 1, 2021): 40002. http://dx.doi.org/10.1209/0295-5075/ac4dd4.

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Abstract Diffusion in a logarithmic potential (DLP) attracted significant interest in physics recently. The dynamics of DLP are governed by a Langevin stochastic differential equation (SDE) whose underpinning potential is logarithmic, and that is driven by Brownian motion. The SDE that governs DLP is a particular case of a selfsimilar SDE: one that is driven by a selfsimilar motion, and that produces a selfsimilar motion. This paper establishes the pivotal role of selfsimilar SDEs via two novel universality results. I) Selfsimilar SDEs emerge universally, on the macro level, when applying scaling limits to micro-level SDEs. II) Selfsimilar SDEs emerge universally when applying the Lamperti transformation to stationary SDEs. Using the universality results, this paper further establishes: a novel statistical-analysis approach to selfsimilar Ito diffusions; and the focal importance of DLP.
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11

Malinowski, Marek T., and Mariusz Michta. "Stochastic set differential equations." Nonlinear Analysis: Theory, Methods & Applications 72, no. 3-4 (February 2010): 1247–56. http://dx.doi.org/10.1016/j.na.2009.08.015.

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12

Zhang, Qi, and Huaizhong Zhao. "Mass-conserving stochastic partial differential equations and backward doubly stochastic differential equations." Journal of Differential Equations 331 (September 2022): 1–49. http://dx.doi.org/10.1016/j.jde.2022.05.015.

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13

Zhu, QingFeng, and YuFeng Shi. "Forward-backward doubly stochastic differential equations and related stochastic partial differential equations." Science China Mathematics 55, no. 12 (May 20, 2012): 2517–34. http://dx.doi.org/10.1007/s11425-012-4411-1.

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14

Shardlow, Tony. "Modified Equations for Stochastic Differential Equations." BIT Numerical Mathematics 46, no. 1 (March 2006): 111–25. http://dx.doi.org/10.1007/s10543-005-0041-0.

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15

Iddrisu, Wahab A., Inusah Iddrisu, and Abdul-Karim Iddrisu. "Modeling Cholera Epidemiology Using Stochastic Differential Equations." Journal of Applied Mathematics 2023 (May 9, 2023): 1–17. http://dx.doi.org/10.1155/2023/7232395.

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In this study, we extend Codeço’s classical SI-B epidemic and endemic model from a deterministic framework into a stochastic framework. Then, we formulated it as a stochastic differential equation for the number of infectious individuals I t under the role of the aquatic environment. We also proved that this stochastic differential equation (SDE) exists and is unique. The reproduction number, R 0 , was derived for the deterministic model, and qualitative features such as the positivity and invariant region of the solution, the two equilibrium points (disease-free and endemic equilibrium), and stabilities were studied to ensure the biological meaningfulness of the model. Numerical simulations were also carried out for the stochastic differential equation (SDE) model by utilizing the Euler-Maruyama numerical method. The method was used to simulate the sample path of the SI-B stochastic differential equation for the number of infectious individuals I t , and the findings showed that the sample path or trajectory of the stochastic differential equation for the number of infectious individuals I t is continuous but not differentiable and that the SI-B stochastic differential equation model for the number of infectious individuals I t fluctuates inside the solution of the SI-B ordinary differential equation model. Another significant feature of our proposed SDE model is its simplicity.
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16

Yang, Fang, Chen Fang, and Xu Sun. "Marcus Stochastic Differential Equations: Representation of Probability Density." Mathematics 12, no. 19 (September 25, 2024): 2976. http://dx.doi.org/10.3390/math12192976.

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Marcus stochastic delay differential equations are often used to model stochastic dynamical systems with memory in science and engineering. It is challenging to study the existence, uniqueness, and probability density of Marcus stochastic delay differential equations, due to the fact that the delays cause very complicated correction terms. In this paper, we identify Marcus stochastic delay differential equations with some Marcus stochastic differential equations without delays but subject to extra constraints. This helps us to obtain the following two main results: (i) we establish a sufficient condition for the existence and uniqueness of the solution to the Marcus delay differential equations; and (ii) we establish a representation formula for the probability density of the Marcus stochastic delay differential equations. In the representation formula, the probability density for Marcus stochastic differential equations with memory is analytically expressed in terms of probability density for the corresponding Marcus stochastic differential equations without memory.
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17

BAKHTIN, YURI, and JONATHAN C. MATTINGLY. "STATIONARY SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH MEMORY AND STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS." Communications in Contemporary Mathematics 07, no. 05 (October 2005): 553–82. http://dx.doi.org/10.1142/s0219199705001878.

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We explore Itô stochastic differential equations where the drift term possibly depends on the infinite past. Assuming the existence of a Lyapunov function, we prove the existence of a stationary solution assuming only minimal continuity of the coefficients. Uniqueness of the stationary solution is proven if the dependence on the past decays sufficiently fast. The results of this paper are then applied to stochastically forced dissipative partial differential equations such as the stochastic Navier–Stokes equation and stochastic Ginsburg–Landau equation.
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18

Herdiana, Ratna. "NUMERICAL SIMULATION OF STOCHASTIC DIFFERENTIAL EQUATIONS USING IMPLICIT MILSTEIN METHOD." Journal of Fundamental Mathematics and Applications (JFMA) 3, no. 1 (June 10, 2020): 72–83. http://dx.doi.org/10.14710/jfma.v3i1.7416.

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Stiff stochastic differential equations arise in many applications including in the area of biology. In this paper, we present numerical solution of stochastic differential equations representing the Malthus population model and SIS epidemic model, using the improved implicit Milstein method of order one proposed in [6]. The open source programming language SCILAB is used to perform the numerical simulations. Results show that the method is more accurate and stable compared to the implicit Euler method.
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19

Barles, Guy, Rainer Buckdahn, and Etienne Pardoux. "Backward stochastic differential equations and integral-partial differential equations." Stochastics and Stochastic Reports 60, no. 1-2 (February 1997): 57–83. http://dx.doi.org/10.1080/17442509708834099.

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20

Zhu, Jie. "The Mean Field Forward Backward Stochastic Differential Equations and Stochastic Partial Differential Equations." Pure and Applied Mathematics Journal 4, no. 3 (2015): 120. http://dx.doi.org/10.11648/j.pamj.20150403.20.

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21

Zhu, Qingfeng, and Yufeng Shi. "Backward doubly stochastic differential equations with jumps and stochastic partial differential-integral equations." Chinese Annals of Mathematics, Series B 33, no. 1 (January 2012): 127–42. http://dx.doi.org/10.1007/s11401-011-0686-8.

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22

van den Berg, Imme. "Functional Solutions of Stochastic Differential Equations." Mathematics 12, no. 8 (April 21, 2024): 1258. http://dx.doi.org/10.3390/math12081258.

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We present an integration condition ensuring that a stochastic differential equation dXt=μ(t,Xt)dt+σ(t,Xt)dBt, where μ and σ are sufficiently regular, has a solution of the form Xt=Z(t,Bt). By generalizing the integration condition we obtain a class of stochastic differential equations that again have a functional solution, now of the form Xt=Z(t,Yt), with Yt an Ito process. These integration conditions, which seem to be new, provide an a priori test for the existence of functional solutions. Then path-independence holds for the trajectories of the process. By Green’s Theorem, it holds also when integrating along any piece-wise differentiable path in the plane. To determine Z at any point (t,x), we may start at the initial condition and follow a path that is first horizontal and then vertical. Then the value of Z can be determined by successively solving two ordinary differential equations. Due to a Lipschitz condition, this value is unique. The differential equations relate to an earlier path-dependent approach by H. Doss, which enables the expression of a stochastic integral in terms of a differential process.
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23

Rhodes, Remi. "Stochastic Homogenization of Reflected Stochastic Differential Equations." Electronic Journal of Probability 15 (2010): 989–1023. http://dx.doi.org/10.1214/ejp.v15-776.

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24

Shmerling, Efraim. "Asymptotic stability condition for stochastic Markovian systems of differential equations." Mathematica Bohemica 135, no. 4 (2010): 443–48. http://dx.doi.org/10.21136/mb.2010.140834.

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25

Delbaen, Freddy, and Shanjian Tang. "Harmonic analysis of stochastic equations and backward stochastic differential equations." Probability Theory and Related Fields 146, no. 1-2 (December 12, 2008): 291–336. http://dx.doi.org/10.1007/s00440-008-0191-5.

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26

QIAO, HUIJIE, and JINQIAO DUAN. "TOPOLOGICAL EQUIVALENCE FOR DISCONTINUOUS RANDOM DYNAMICAL SYSTEMS AND APPLICATIONS." Stochastics and Dynamics 14, no. 01 (December 29, 2013): 1350007. http://dx.doi.org/10.1142/s021949371350007x.

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After defining non-Gaussian Lévy processes for two-sided time, stochastic differential equations with such Lévy processes are considered. Solution paths for these stochastic differential equations have countable jump discontinuities in time. Topological equivalence (or conjugacy) for such an Itô stochastic differential equation and its transformed random differential equation is established. Consequently, a stochastic Hartman–Grobman theorem is proved for the linearization of the Itô stochastic differential equation. Furthermore, for Marcus stochastic differential equations, this topological equivalence is used to prove the existence of global random attractors.
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27

Sengul, Suleyman, Zafer Bekiryazici, and Mehmet Merdan. "Wong-Zakai method for stochastic differential equations in engineering." Thermal Science 25, Spec. issue 1 (2021): 131–42. http://dx.doi.org/10.2298/tsci200528014s.

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In this paper, Wong-Zakai approximation methods are presented for some stochastic differential equations in engineering sciences. Wong-Zakai approximate solutions of the equations are analyzed and the numerical results are compared with results from popular approximation schemes for stochastic differential equations such as Euler-Maruyama and Milstein methods. Several differential equations from engineering problems containing stochastic noise are investigated as numerical examples. Results show that Wong-Zakai method is a reliable tool for studying stochastic differential equations and can be used as an alternative for the known approximation techniques for stochastic models.
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28

Johansyah, Muhamad Deni, Endang Rusyaman, Bob Foster, Khoirunnisa Rohadatul Aisy Muslihin, and Asep K. Supriatna. "Combining Differential Equations with Stochastic for Economic Growth Models in Indonesia: A Comprehensive Literature Review." Mathematics 12, no. 20 (October 14, 2024): 3219. http://dx.doi.org/10.3390/math12203219.

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Economic growth modeling is one of the methods a government can use to formulate appropriate economic policies to improve the prosperity of its people. Differential equations and stochastic models play a major role in studying economic growth. This article aims to conduct a literature review on the use of differential equations in relation to stochastics to model economic growth. In addition, this article also discusses the use of differential and stochastic equations in economic growth models in Indonesia. This study involves searching for and selecting articles to obtain a collection of research works relevant to the application of differential and stochastic equations to economic growth models, supported by bibliometric analysis. The results of this literature review show that there is still little research discussing economic growth models using differential equations combined with stochastic models, especially those applied in Indonesia. While the application of these models remains relatively limited, their potential to offer deeper insights into the complex dynamics of economic growth is undeniable. By further developing and refining these models, we can gain a more comprehensive understanding of the factors driving growth and the potential implications of various economic policies. This will ultimately equip policy-makers with a more powerful analytical tool for making informed decisions.
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29

Fleming, W. H., and M. Nisio. "Differential games for stochastic partial differential equations." Nagoya Mathematical Journal 131 (September 1993): 75–107. http://dx.doi.org/10.1017/s0027763000004554.

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In this paper we are concerned with zero-sum two-player finite horizon games for stochastic partial differential equations (SPDE in short). The main aim is to formulate the principle of dynamic programming for the upper (or lower) value function and investigate the relationship between upper (or lower) value function and viscocity solution of min-max (or max-min) equation on Hilbert space.
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30

Huang, Xing, Panpan Ren, and Feng-Yu Wang. "Distribution dependent stochastic differential equations." Frontiers of Mathematics in China 16, no. 2 (April 2021): 257–301. http://dx.doi.org/10.1007/s11464-021-0920-y.

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31

Hasan, Ali, Joao M. Pereira, Sina Farsiu, and Vahid Tarokh. "Identifying Latent Stochastic Differential Equations." IEEE Transactions on Signal Processing 70 (2022): 89–104. http://dx.doi.org/10.1109/tsp.2021.3131723.

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32

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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33

KIM, JAI HEUI. "ON FUZZY STOCHASTIC DIFFERENTIAL EQUATIONS." Journal of the Korean Mathematical Society 42, no. 1 (January 1, 2005): 153–69. http://dx.doi.org/10.4134/jkms.2005.42.1.153.

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34

Shevchenko, G. "Mixed stochastic delay differential equations." Theory of Probability and Mathematical Statistics 89 (January 26, 2015): 181–95. http://dx.doi.org/10.1090/s0094-9000-2015-00944-3.

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35

Nand Kumar. "Stochastic Differential Equations in Physics." Communications on Applied Nonlinear Analysis 31, no. 4s (July 5, 2024): 433–39. http://dx.doi.org/10.52783/cana.v31.937.

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Stochastic Differential Equations (SDEs) are powerful mathematical tools used to model systems subject to random fluctuations. In physics, SDEs find widespread applications ranging from statistical mechanics to quantum field theory. This paper provides an in-depth exploration of the theoretical foundations of SDEs in physics, their applications, and their implications in understanding complex physical phenomena. We delve into the mathematical framework of SDEs, their numerical solutions, and their role in modeling various physical processes. Furthermore, we present case studies illustrating the practical relevance of SDEs in different branches of physics.
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36

Detering, Nils, Jean-Pierre Fouque, and Tomoyuki Ichiba. "Directed chain stochastic differential equations." Stochastic Processes and their Applications 130, no. 4 (April 2020): 2519–51. http://dx.doi.org/10.1016/j.spa.2019.07.009.

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37

Janković, Svetlana, Miljana Jovanović, and Jasmina Djordjević. "Perturbed backward stochastic differential equations." Mathematical and Computer Modelling 55, no. 5-6 (March 2012): 1734–45. http://dx.doi.org/10.1016/j.mcm.2011.11.018.

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38

Saito, Yoshihiro, and Taketomo Mitsui. "Simulation of stochastic differential equations." Annals of the Institute of Statistical Mathematics 45, no. 3 (1993): 419–32. http://dx.doi.org/10.1007/bf00773344.

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39

Kargin, Vladislav. "On Free Stochastic Differential Equations." Journal of Theoretical Probability 24, no. 3 (January 26, 2011): 821–48. http://dx.doi.org/10.1007/s10959-011-0341-z.

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40

Benaroya, H. "Stationarity and stochastic differential equations." Applied Mathematical Modelling 14, no. 12 (December 1990): 649–54. http://dx.doi.org/10.1016/0307-904x(90)90024-y.

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41

Higham, D. J., and X. Mao. "Nonnormality and stochastic differential equations." BIT Numerical Mathematics 46, no. 3 (August 16, 2006): 525–32. http://dx.doi.org/10.1007/s10543-006-0067-y.

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42

Bass, Richard F. "Stochastic differential equations with jumps." Probability Surveys 1 (2004): 1–19. http://dx.doi.org/10.1214/154957804100000015.

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43

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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44

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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45

Motamed, Mohammad. "Fuzzy-Stochastic Partial Differential Equations." SIAM/ASA Journal on Uncertainty Quantification 7, no. 3 (January 2019): 1076–104. http://dx.doi.org/10.1137/17m1140017.

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46

Antonelli, Fabio. "Backward-Forward Stochastic Differential Equations." Annals of Applied Probability 3, no. 3 (August 1993): 777–93. http://dx.doi.org/10.1214/aoap/1177005363.

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47

Janković, Svetlana, and Miljana Jovanović. "Perturbed stochastic hereditary differential equations." Stochastic Analysis and Applications 20, no. 3 (January 1, 2002): 567–89. http://dx.doi.org/10.1081/sap-120004115.

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48

Ermakov, Sergej M., and Anna A. Pogosian. "On solving stochastic differential equations." Monte Carlo Methods and Applications 25, no. 2 (June 1, 2019): 155–61. http://dx.doi.org/10.1515/mcma-2019-2038.

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Abstract This paper proposes a new approach to solving Ito stochastic differential equations. It is based on the well-known Monte Carlo methods for solving integral equations (Neumann–Ulam scheme, Markov chain Monte Carlo). The estimates of the solution for a wide class of equations do not have a bias, which distinguishes them from estimates based on difference approximations (Euler, Milstein methods, etc.).
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49

Lindsay, J. Martin, and Adam G. Skalski. "On quantum stochastic differential equations." Journal of Mathematical Analysis and Applications 330, no. 2 (June 2007): 1093–114. http://dx.doi.org/10.1016/j.jmaa.2006.07.105.

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50

Buckdahn, Rainer. "Linear skorohod stochastic differential equations." Probability Theory and Related Fields 90, no. 2 (June 1991): 223–40. http://dx.doi.org/10.1007/bf01192163.

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