Stochastic Taylor Expansions for Functionals of Diffusion Processes
Probability
2013-10-24 v1
Abstract
In the present paper, a stochastic Taylor expansion of some functional applied to the solution process of an It\^o or Stratonovich stochastic differential equation with a multi-dimensional driving Wiener process is given. Therefore, the multi-colored rooted tree analysis is applied in order to obtain a transparent representation of the expansion which is similar to the B-series expansion for solutions of ordinary differential equations in the deterministic setting. Further, some estimates for the mean--square and the mean truncation errors are given.
Cite
@article{arxiv.1310.6181,
title = {Stochastic Taylor Expansions for Functionals of Diffusion Processes},
author = {Andreas Rößler},
journal= {arXiv preprint arXiv:1310.6181},
year = {2013}
}