Solving stochastic differential equations with Cartan's exterior differential systems
Probability
2014-04-21 v1
Abstract
The aim of this work is to use systematically the symmetries of the (one dimensional) bacward heat equation with potentiel in order to solve certain one dimensional It\^o's stochastic differential equations. The special form of the drift (suggested by quantum mechanical considerations) gives, indeed, access to an algebrico-geometric method due, in essence, to E.Cartan, and called the Method of Isovectors. A V singular at the origin, as well as a one-factor affine model relevant to stochastic finance, are considered as illustrations of the method.
Cite
@article{arxiv.1404.4802,
title = {Solving stochastic differential equations with Cartan's exterior differential systems},
author = {Paul Lescot and Hélène Quintard and Jean-Claude Zambrini},
journal= {arXiv preprint arXiv:1404.4802},
year = {2014}
}