Reflected solutions of backward doubly SDEs driven by Brownian motion and Poisson random measure

Monia Karouf

doi:10.3934/dcds.2019245

Article Contents

2019, Volume 39, Issue 10: 5571-5601. Doi: 10.3934/dcds.2019245

This issue Previous Article Propagation of long-crested water waves. Ⅱ. Bore propagation Next Article Standing and travelling waves in a parabolic-hyperbolic system

Reflected solutions of backward doubly SDEs driven by Brownian motion and Poisson random measure

Monia Karouf

Higher Institute of Applied Sciences and Technologies of Gabès & LR17ES11, Tunisia

Received: February 28, 2018

Revised: March 31, 2019

Published: July 2019

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Abstract

We consider backward doubly stochastic differential equations (BDSDEs in short) driven by a Brownian motion and an independent Poisson random measure. We give sufficient conditions for the existence and the uniqueness of solutions of equations with Lipschitz generator which is, first, standard and then depends on the values of a solution in the past. We also prove comparison theorem for reflected BDSDEs.

Keywords:

Backward doubly stochastic differential equations,
time delayed generators,
Poisson point process,
Mokobodski's hypothesis,
Snell envelope,
fixed point theorem,
comparison theorem.

Mathematics Subject Classification: Primary: 60H10, 60H20, 60G55, 60G57; Secondary: 34K12, 60G40.

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