Backward doubly stochastic differential equations driven by Brownian motions and Poisson process(BDSDEP) with non-Lipschitz coeffcients on random time interval are studied.The probabilistic interpretation for the solutions to a class of quasilinear stochastic partial differential-integral equations(SPDIEs) is treated with BDSDEP.Under non-Lipschitz conditions,the existence and uniqueness results for measurable solutions to BDSDEP are established via the smoothing technique.Then,the continuous dependence for solutions to BDSDEP is derived.Finally,the probabilistic interpretation for the solutions to a class of quasilinear SPDIEs is given.
This paper is devoted to the unique solvability of backward stochastic Volterra integral equations （BSVIEs, for short）, in terms of both M-solution and the adapted solutions. We prove the existence and uniqueness of M-solutions of BSVIEs in Lp （1 〈 p 〈 2）, which extends the existing results on M-solutions. The unique solvability of adapted solutions of BSVIEs in Lp （p 〉 1） is also considered, which also generalizes the results in the existing literature.
