Martingale Decomposition and Backward Stochastic Dynamic Equations on Time Scales

Abstract

The paper aims to establish the related backward stochastic dynamic equations on time scales, BS $\nabla$ Es for short, concerning to $\nabla$ -integral on time scales. We present the martingale decomposition theorem on time scales and prove the existence and uniqueness theorem of solutions to BS $\nabla$ Es. This work can be considered as a unification and a generalization of similar results in backward stochastic difference equations and backward stochastic differential equations.