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Modern Stochastics: Theory and Applications


Irregular barrier reflected BDSDEs with general jumps under stochastic Lipschitz and linear growth conditions
Volume 7, Issue 2 (2020), pp. 157–190
Pub. online: 10 June 2020      Type: Research Article      Open accessOpen Access
Received
6 March 2020
Revised
5 May 2020
Accepted
29 May 2020
Published
10 June 2020

Abstract

In this paper, a solution is given to reflected backward doubly stochastic differential equations when the barrier is not necessarily right-continuous, and the noise is driven by two independent Brownian motions and an independent Poisson random measure. The existence and uniqueness of the solution is shown, firstly when the coefficients are stochastic Lipschitz, and secondly by weakening the conditions on the stochastic growth coefficient.

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© 2020 The Author(s). Published by VTeX
Open access article under the CC BY license.

Keywords
Reflected backward doubly stochastic differential equations irregular barrier Mertens decomposition stochastic Lipschitz condition stochastic linear growth condition

MSC2010
60H20 60H30

Funding
The corresponding author (Mohamed Marzougue) declares that this research was supported by National Center for Scientific and Technical Research (CNRST), Morocco.

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