Pathwise definition of second-order SDEs

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Quer-Sardanyons, Lluis¹  Tindel, Samy² 

[1] Univ Autonoma Barcelona, Dept Matemat, Fac Ciencias, Bellaterra 08193, Spain

[2] Inst Elie Cartan Nancy, F-54506 Vandoeuvre Les Nancy, France

关键词: Elliptic SPDEs;    Young integration;    Fractional Brownian motion;    Malliavin calculus;   

DOI  :  10.1016/j.spa.2011.08.014

来源: Elsevier

【 摘 要 】

In this article, a class of second-order differential equations on [0, 1], driven by a gamma-Holder continuous function for any value of gamma is an element of (0, 1) and with multiplicative noise, is considered. We first show how to solve this equation in a pathwise manner, thanks to Young integration techniques. We then study the differentiability of the solution with respect to the driving process and consider the case where the equation is driven by a fractional Brownian motion, with two aims in mind: show that the solution that we have produced coincides with the one which would be obtained with Malliavin calculus tools, and prove that the law of the solution is absolutely continuous with respect to the Lebesgue measure. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free