Solving stochastic differential equations with Cartan's exterior differential systems

Paul Lescot; Hélène Quintard; Jean-Claude Zambrini

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arXiv · 1404.4802

Solving stochastic differential equations with Cartan's exterior differential systems

Paul Lescot·Hélène Quintard·Jean-Claude Zambrini

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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 Itô'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.

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Paul Lescot, Hélène Quintard, Jean-Claude Zambrini. 2014-04-18. Solving stochastic differential equations with Cartan's exterior differential systems. https://arxiv.org/abs/1404.4802

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