Reduction and reconstruction of stochastic differential equations via symmetries
Probability
2020-08-04 v1 Mathematical Physics
math.MP
Abstract
An algorithmic method to exploit a general class of infinitesimal symmetries for reducing stochastic differential equations is presented and a natural definition of reconstruction, inspired by the classical reconstruction by quadratures, is proposed. As a side result the well-known solution formula for linear one-dimensional stochastic differential equations is obtained within this symmetry approach. The complete procedure is applied to several examples with both theoretical and applied relevance.
Keywords
Cite
@article{arxiv.1607.08556,
title = {Reduction and reconstruction of stochastic differential equations via symmetries},
author = {Francesco C. De Vecchi and Paola Morando and Stefania Ugolini},
journal= {arXiv preprint arXiv:1607.08556},
year = {2020}
}