Functional integrals method for systems of stochastic differential equations
https://doi.org/10.29235/1561-2430-2018-54-3-279-289
Abstract
Systems of stochastic differential equations, for which the Riemannian manifold generated by a diffusion matrix has zero curvature, are considered in this article. The method for approximate evaluation of characteristics of the solution of the systems of stochastic differential equations is proposed. This method is based on the representation of the probability density function through the functional integral. To compute functional integrals we use the expansion of action with respect to a classical trajectory, for which the action takes an extreme value. The classical trajectory is found as the solution of the multidimensional Euler – Lagrange equation.
About the Authors
E. A. Ayryan
Joint Institute for Nuclear Research
Russian Federation
Russian Federation
Edik A. Ayryan – Ph. D. (Physics and Mathematics), Head of the Sector of the Laboratory of Information Technologies.
6, Joliot-Curie Str., 141980, Dubna.
A. D. Egorov
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Alexandr D. Egorov – D. Sc. (Physics and Mathematics), Chief Researcher.
11, Surganov Str., 220072, Minsk.
D. S. Kulyabov
Joint Institute for Nuclear Research; RUDN University
Russian Federation
Russian Federation
Dmitry S. Kulyabov – D. Sc. (Physics and Mathema- tics), Assistant Professor, Department of Applied Probability and Informatics, RUDN University.
6, Mikluho-Maklaya Str., 117198, Moscow.
V. B. Malyutin
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Victor B. Malyutin – D. Sc. (Physics and Mathematics), Leading Researcher.
11, Surganov Str., 220072, Minsk.
L. A. Sevastyanov
Joint Institute for Nuclear Research; RUDN University
Russian Federation
Russian Federation
Leonid A. Sevastyanov – D. Sc. (Physics and Mathematics), Professor, Department of Applied Probability and In- formatics, RUDN University.
6, Mikluho-Maklaya Str., 117198, Moscow.
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