Geodesic
Application of functional integrals to stochastic equations
Matematičeskoe modelirovanie, Tome 28 (2016) no. 11, pp. 113-125

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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. 
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     author = {E. A. Ayryan and A. D. Egorov and D. S. Kulyabov and V. B. Malyutin and L. A. Sevastyanov},
     title = {Application of functional integrals to stochastic equations},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {113--125},
     publisher = {mathdoc},
     volume = {28},
     number = {11},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2016_28_11_a7/}
}
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E. A. Ayryan; A. D. Egorov; D. S. Kulyabov; V. B. Malyutin; L. A. Sevastyanov. Application of functional integrals to stochastic equations. Matematičeskoe modelirovanie, Tome 28 (2016) no. 11, pp. 113-125. http://geodesic.mathdoc.fr/item/MM_2016_28_11_a7/