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.