2012/08/10 by Tianxiao Wang, Wang, Tianxiao, Jiongmin Yong +1
Economics, Econometrics and Finance · Mathematics · #60H10 #60H20 #91G80 #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1208.2064
openalex publication_date 2012/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For backward stochastic Volterra integral equations (BSVIEs) in multi-dimensional Euclidean spaces, comparison theorems are established in a systematic way for the adapted solutions and adapted M-solutions. For completeness, comparison theorems for (forward) stochastic differential equations, backward stochastic differential equations, and (forward) stochastic Volterra integral equations (FSVIEs) are also presented. Duality principles are used in some relevant proofs. Also, it is found that certain kind of monotonicity conditions play crucial roles to guarantee the comparison theorems for FSVIEs and BSVIEs to be true. Various counterexamples show that the assumed conditions are almost necessary in some sense.