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Finite and Infinite Time Interval of BDSDEs Driven by Lévy Processes

Volume 13, Number 2 (2012), 108 - 126

Finite and Infinite Time Interval of BDSDEs Driven by Lévy Processes

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Abstract

In this work we deal with a backward doubly stochastic differential equation (BDSDE) associated to a Poisson random measure. We establish existence and uniqueness of solution in the case of non-Lipschitz coefficients. The novelty of our result lies in the fact that we allow the time interval to be infinite.