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 Access
Open Access
Received
6 March 2020
6 March 2020
Revised
5 May 2020
5 May 2020
Accepted
29 May 2020
29 May 2020
Published
10 June 2020
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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