Martingale Decomposition and Backward Stochastic Dynamic Equations on Time Scales

The paper aims to establish the related backward stochastic dynamic equations on time scales, BS backward difference Es for short, concerning to backward difference -integral on time scales. We present the martingale decomposition theorem on time scales and prove the existence and uniqueness theorem of solutions to BS backward difference 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.