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Matematicheskoe modelirovanie, 2016, Volume 28, Number 11, Pages 113–125 (Mi mm3790)  
This article is cited in 5 scientific papers (total 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
Full-text PDF (332 kB) Citations (5)
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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.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00628_а
15-07-08795_а
Belarusian Republican Foundation for Fundamental Research Ф14Д-002
Received: 12.05.2015
English version:
Mathematical Models and Computer Simulations, 2017, Volume 9, Issue 3, Pages 339–348
DOI: https://doi.org/10.1134/S2070048217030024
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: E. A. Ayryan, A. D. Egorov, D. S. Kulyabov, V. B. Malyutin, L. A. Sevastyanov, “Application of functional integrals to stochastic equations”, Matem. Mod., 28:11 (2016), 113–125; Math. Models Comput. Simul., 9:3 (2017), 339–348
Citation in format AMSBIB
\Bibitem{HayEgoKul16}
\by E.~A.~Ayryan, A.~D.~Egorov, D.~S.~Kulyabov, V.~B.~Malyutin, L.~A.~Sevastyanov
\paper Application of functional integrals to stochastic equations
\jour Matem. Mod.
\yr 2016
\vol 28
\issue 11
\pages 113--125
\mathnet{http://mi.mathnet.ru/mm3790}
\elib{https://elibrary.ru/item.asp?id=28119130}
\transl
\jour Math. Models Comput. Simul.
\yr 2017
\vol 9
\issue 3
\pages 339--348
\crossref{https://doi.org/10.1134/S2070048217030024}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85020164995}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математическое моделирование
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