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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Submitted on : Saturday, June 23, 2018 - 5:54:09 PM
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  • HAL Id : hal-01820593, version 2

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Rama Cont, Alexander Kalinin. On the support of solutions of stochastic differential equations with path-dependent coefficients. 2018. ⟨hal-01820593v2⟩

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