Comparison Theorems For Some Backward Stochastic Volterra Integral Equations

Keywords

Backward stochastic Volterra integral equation; Comparison theorem; Duality principle; Forward stochastic Volterra integral equations

Abstract

For some 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 kinds 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.

Publication Date

1-1-2015

Publication Title

Stochastic Processes and their Applications

Volume

125

Issue

5

Number of Pages

1756-1798

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.spa.2014.11.013

Socpus ID

85027940255 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85027940255

This document is currently not available here.

Share

COinS