On the support of solutions to stochastic differential equations with path-dependent coefficients

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Cont, Rama¹  Kalinin, Alexander² 

[1] Univ Oxford, Math Inst, Oxford, England

[2] Imperial Coll London, Dept Math, London, England

关键词: Support theorem;    Stochastic differential equation;    Functional equation;    Semimartingale;    Wiener space;    Functional Ito calculus;   

DOI  :  10.1016/j.spa.2019.07.015

来源: Elsevier

【 摘 要 】

Given a stochastic differential equation with path-dependent coefficients driven by a multidimensional Wiener process, we show that the support of the law of the solution is given by the image of the Cameron-Martin space under the flow of mild solutions to a system of path-dependent ordinary differential equations. Our result extends the Stroock-Varadhan support theorem for diffusion processes to the case of SDEs with path-dependent coefficients. The proof is based on functional Ito calculus. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free