L ^p Solutions for Multidimensional BDSDEs with Locally Weak Monotonicity Coefficients

Abstract

In this paper, the authors establish the existence and uniqueness theorem of L ^p (1 < p ≤ 2) solutions for multidimensional backward doubly stochastic differential equations (BDSDEs for short) under the p-order globally (locally) weak monotonicity conditions. Comparison theorem of L ^p solutions for one-dimensional BDSDEs is also proved. These conclusions unify and generalize some known results.

Keywords

Backward doubly stochastic differential equation / Locally monotonicity condition / L ^p solution