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On the support of solutions to stochastic differential equations with path-dependent coefficients.
- Source :
-
Stochastic Processes & Their Applications . May2020, Vol. 130 Issue 5, p2639-2674. 36p. - Publication Year :
- 2020
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03044149
- Volume :
- 130
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Stochastic Processes & Their Applications
- Publication Type :
- Academic Journal
- Accession number :
- 142440845
- Full Text :
- https://doi.org/10.1016/j.spa.2019.07.015