2020/12/21 by Guofeng Tang, Tang, Guofeng
Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2012.11200
openalex publication_date 2020/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we present martingale decomposition on time scales. We establish the related backward stochastic dynamic equations on time scales (this paper BS∇E for short, concerning ∇-integral on time scales) which unify backward stochastic differential equations and backward stochastic difference equations. We prove the existence and uniqueness theorem of BS∇E. This work can be considered as a unification and a generalization of similar results in backward stochastic difference equations and backward stochastic differential equations.