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

Abstract : Given a stochastic differential equation with path-dependent coefficients driven by a multidimensional Wiener process, we show that the topological support in Holder norm of the law of the solution is given by the image of the Cameron-Martin space under the flow of the solutions of 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 the Functional Ito calculus and interpolation estimates in Holder norm.
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https://hal.archives-ouvertes.fr/hal-01820593
Contributor : Rama Cont <>
Submitted on : Thursday, June 21, 2018 - 10:57:04 PM
Last modification on : Wednesday, April 8, 2020 - 1:40:03 PM
Long-term archiving on: : Tuesday, September 25, 2018 - 6:04:35 PM

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  • HAL Id : hal-01820593, version 1

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Rama Cont, Alexander Kalinin. On the support of solutions of stochastic differential equations with path-dependent coefficients. 2018. ⟨hal-01820593v1⟩

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