Lp (1 < p < 2) solutions of backward doubly stochastic differential equations with locally monotone coefficients

Abstract

The article considers the existence and uniqueness of solutions for backward doubly stochastic differential equations (BDSDEs) under globally (locally) monotone conditions. Some useful and important prior estimates are established. By using truncation method, Lp solutions for BDSDEs under globally monotone assumptions are obtained. With the help of suitable approximation techniques, we derive the existence and uniqueness of Lp solutions for BDSDEs with locally monotone coefficients.