Anticipated Backward Doubly Stochastic Differential Equations with Non-Lipschitz Coefficients

Tie Wang and Siyu Cui
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Tie Wang: School of Mathematics, Liaoning University, Shenyang 110036, China
Siyu Cui: School of Mathematics, Liaoning University, Shenyang 110036, China

Mathematics, 2022, vol. 10, issue 3, 1-18

Abstract: The work presented in this paper focuses on a type of differential equations called anticipated backward doubly stochastic differential equations (ABDSDEs) whose generators not only depend on the anticipated terms of the solution ( Y · , Z · ) but also satisfy one kind of non-Lipschitz assumption. Firstly, we give the existence and uniqueness theorem. Further, two comparison theorems for the solutions of these equations are obtained after finding a new comparison theorem for backward doubly stochastic differential equations (BDSDEs) with non-Lipschitz coefficients.

Keywords: anticipated backward doubly stochastic differential equations; comparison theorems; non-Lipschitz coefficients (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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