Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [21 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01820593
Contributor : Rama Cont <>
Submitted on : Saturday, June 23, 2018 - 5:54:09 PM
Last modification on : Friday, April 10, 2020 - 5:13:33 PM
Document(s) archivé(s) le : Wednesday, September 26, 2018 - 8:32:57 PM

File

SupportTheorem.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01820593, version 2

Citation

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

Share

Metrics

Record views

372

Files downloads

845