BDSDE with Poisson jumps under stochastic Lipschitz and linear growth conditions

摘要

In this paper, we deal with a backward doubly stochastic differential equations with jumps. Under stochastic Lipschitz conditions on the coefficients, we prove the existence and uniqueness of solution and provide a comparison theorem. Using this comparison theorem, we show the existence of a minimal solution when the drift satisfy a stochastic growth condition.