Backward doubly stochastic differential equations driven by fractional Brownian motion with stochastic integral-Lipschitz coefficients. (English) Zbl 07812407
Summary: This paper deals with a class of backward doubly stochastic differential equations driven by fractional Brownian motion with Hurst parameter \(H\) greater than \(\frac{1}{2}\). We essentially establish the existence and uniqueness of a solution in the case of stochastic Lipschitz coefficients and stochastic integral-Lipschitz coefficients. The stochastic integral used throughout the paper is the divergence-type integral.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60H05 | Stochastic integrals |
| 60H07 | Stochastic calculus of variations and the Malliavin calculus |
| 60G22 | Fractional processes, including fractional Brownian motion |
Keywords:
backward doubly stochastic differential equation; stochastic Lipschitz coefficients; Malliavin derivative and fractional Itô formulaReferences:
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