On the support of solutions of stochastic differential equations with path-dependent coefficients
Probability
2019-09-05 v2 Functional Analysis
Abstract
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 stochastic differential equations with path-dependent coefficients. The proof is based on functional Ito calculus.
Keywords
Cite
@article{arxiv.1806.08988,
title = {On the support of solutions of stochastic differential equations with path-dependent coefficients},
author = {Rama Cont and Alexander Kalinin},
journal= {arXiv preprint arXiv:1806.08988},
year = {2019}
}
Comments
42 pages