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 Lp , for any p ∈ ( 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.