Homotopy analysis method for stochastic differential equations
Abstract
The homotopy analysis method known from its successful applications to obtain quasi-analytical approximations of solutions of ordinary and partial differential equations is applied to stochastic differential equations with Gaussian stochastic forces and to the Fokker-Planck equations. Only the simplest non-trivial examples of such equations are considered, but such that they can almost immediately be translated to those which appear in the stochastic quantization of a nonlinear scalar field theory. It has been found that the homotopy analysis method yields excellent agreement with exact results (when the latter are available) and appears to be a very promising approach in the calculations related to quantum field theory and quantum statistical mechanics.
Keywords
Cite
@article{arxiv.1410.1715,
title = {Homotopy analysis method for stochastic differential equations},
author = {Maciej Janowicz and Filip Krzyżewski and Joanna Kaleta and Marian Rusek and Arkadiusz Orłowski},
journal= {arXiv preprint arXiv:1410.1715},
year = {2014}
}