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JOURNALS // Matematicheskoe modelirovanie // Archive

Mat. Model., 2016 Volume 28, Number 11, Pages 113–125 (Mi mm3790)

This article is cited in 5 papers

Application of functional integrals to stochastic equations

E. A. Ayryana, A. D. Egorovb, D. S. Kulyabovca, V. B. Malyutinb, L. A. Sevastyanovcd

a Laboratory of Information Technologies, Joint Institute for Nuclear Research
b Institute of Mathematics, The National Academy of Sciences of Belarus
c Department of Applied Probability and Informatics, Peoples' Friendship University of Russia
d Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research

Abstract: Representation of the probability density function (PDF) and other quantities, describing solution of stochastic differential equation, by means of functional integral is considered in this paper. Method of approximate evaluation of appearing functional integrals is presented. Onsager–Machlup functionals are used to represent PDF by means of functional integral. Using these functionals the expression for PDF on small time interval $\Delta t$ can be written. This expression is true up to terms having order higher than the first in comparison with $\Delta t$. Method of approximate evaluation of appearing functional integrals is considered. This method is based on expansion of action along classical path. As an example the application of proposed method to evaluation of some quantities for solution of equation for the Cox Ingersoll Ross type model is considered.

Keywords: stochastic differential equations, Onsager–Machlup functionals, functional integrals.

Received: 12.05.2015


 English version:
Mathematical Models and Computer Simulations, 2017, 9:3, 339–348

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