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

Rama Cont and Alexander Kalinin

Stochastic Processes and their Applications, 2020, vol. 130, issue 5, 2639-2674

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 SDEs with path-dependent coefficients. The proof is based on functional Itô calculus.

Keywords: Support theorem; Stochastic differential equation; Functional equation; Semimartingale; Wiener space; Functional Itô calculus (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2019.07.015

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