A general type of weak comparison theorems for BDSDEs

Jinghan Wang, Yufeng Shi and Nana Zhao

Statistics & Probability Letters, 2025, vol. 219, issue C

Abstract: In this paper we study a special type of weak comparison theorems for backward doubly stochastic differential equations (BDSDEs, in short). It is worth emphasizing that, unlike the comparison theorems in the previous literature, which all require that the coefficients g(i),i=1,2 of the doubly stochastic integration term must be same, we allow the coefficients g(i),i=1,2 to be different in this paper. In addition, we extend this conclusion to a class of general mean-field backward doubly stochastic differential equations (mean-field BDSDEs, in short), in which the coefficient f not only depends on the solution processes y,z, but also depends on the law of the solution, i.e. μ, which describes the characteristic of the mean-field.

Keywords: Backward doubly stochastic differential equations; Weak comparison theorem; Mean-field; Wasserstein metric (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2024.110353

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