The obstacle problem for semilinear parabolic partial integro-differential equations

Abstract : We give a probabilistic interpretation for the weak Sobolev solution of obstacle problem for semilinear parabolic partial integro-differential equations (PIDE). The results of Léandre [29] about the homeomorphic property for the solution of SDE with jumps are used to construct random test functions for the variational equation for such PIDE. This yields to the natural connection with the associated Reflected Backward Stochastic Differential Equations with jumps (RBSDE), namely the Feynman Kac's formula for the solution of the PIDE. MSC: 60H15; 60G46; 35R60 Keyword: Reflected backward stochastic differential equation, partial parabolic integro-differential equation, jump diffusion process, obstacle problem, stochastic flow, flow of diffeo-morphism.
Complete list of metadatas

Cited literature [46 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01740723
Contributor : Anis Matoussi <>
Submitted on : Thursday, March 22, 2018 - 12:05:42 PM
Last modification on : Friday, July 20, 2018 - 11:13:08 AM
Long-term archiving on : Thursday, September 13, 2018 - 8:33:56 AM

File

PIDE-MSZ-revision.pdf
Files produced by the author(s)

Identifiers

Citation

Anis Matoussi, Wissal Sabbagh, Chao Zhou. The obstacle problem for semilinear parabolic partial integro-differential equations. Stochastics and Dynamics, World Scientific Publishing, 2015, 15 (01), ⟨10.1142/S0219493715500070⟩. ⟨hal-01740723⟩

Share

Metrics

Record views

104

Files downloads

93