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arXiv · 1806.08988

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

Rama Cont·Alexander Kalinin
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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.

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Rama Cont, Alexander Kalinin. 2019-09-04. On the support of solutions of stochastic differential equations with path-dependent coefficients. https://doi.org/10.1016/j.spa.2019.07.015

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