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

Cont, Rama and Kalinin, Alexander (2020): On the support of solutions to stochastic differential equations with path-dependent coefficients. In: Stochastic Processes and their Applications, Vol. 130, No. 5: pp. 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Workgroup Financial Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 03044149
• Language: English