L^p-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.

Keywords:

• Backward doubly stochastic differential equation
• stochastic linear growth
• stochastic Lipschitz-continuous
• comparison theorem
• L^p-Solution

Mathematical Subject Classification:

• 60H05
• 60H10
• 60H20