On the Bounded Variation of the Flow of Stochastic Differential Equation

Conference paper
Part of the Springer Proceedings in Mathematics book series (PROM, volume 7)

Abstract

We consider a stochastic differential equation, driven by a Brownian motion, with non Lipschitz coefficients. We consider the class BV which is larger than Sobolev space and got a sufficient condition for a solution of stochastic differential equation to belong to the class BV. As a consequence we prove that the corresponding flow is, almost surely, almost every where derivable with respect to initial data. The result is a partial extension of the result of N. Bouleau and F. Hirsch on the derivability, with respect to the initial data, of the solution of a stochastic differential equation with Lipschitz coefficients.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

The authors wish to thank the anonymous referee for the suggestion of a simple proof of Lemma 1. This work was supported by the Academy Hassan II of Sciences and Technology

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Faculté des Sciences Semlalia, Département de MathématiquesUniversité Cadi AyyadMarrakechMaroc

Personalised recommendations