L^p-Solutions of backward doubly stochastic differential equations with stochastic Lipschitz condition and p ∈ (1,2)

Université Félix H. Boigny, Cocody, UFR de Mathématiques et Informatique, 22 BP 582 Abidjan, Côte d’Ivoire.
owojm@yahoo.fr

Received: 4 September 2015
Revised: 9 September 2016
Accepted: 24 March 2017

Abstract

We study backward doubly stochastic differential equations where the coefficients satisfy stochastic Lipschitz condition. We prove the existence and uniqueness of the solution in L^p with p ∈ (1,2).