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A general type of weak comparison theorems for BDSDEs

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  • Wang, Jinghan
  • Shi, Yufeng
  • Zhao, Nana

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.

Suggested Citation

  • Wang, Jinghan & Shi, Yufeng & Zhao, Nana, 2025. "A general type of weak comparison theorems for BDSDEs," Statistics & Probability Letters, Elsevier, vol. 219(C).
    • Handle: RePEc:eee:stapro:v:219:y:2025:i:c:s0167715224003225
    DOI: 10.1016/j.spl.2024.110353
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    References listed on IDEAS

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    1. Lepeltier, J. P. & San Martin, J., 1997. "Backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 425-430, April.
    2. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
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