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Pré-Publication, Document De Travail Année : 2018

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

Résumé

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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Dates et versions

hal-01820593 , version 1 (21-06-2018)
hal-01820593 , version 2 (23-06-2018)

Identifiants

  • HAL Id : hal-01820593 , version 2

Citer

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