Lp-Solutions of backward doubly SDEs with continuous and stochastic linear growth coefficients and p ∈ (1,2)

Abstract

In this paper, we are interested in solving backward doubly stochastic differential equations in L^p, for any $p\in (1,2),$ when the coefficients are continuous with stochastic linear growth. Via approximation and comparison theorem, the existence of $L^p-$ minimal and $L^p-$ maximal solutions are obtained.