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April 27, 2026Random Operators and Stochastic Equations0 citations

Fractional delay and anticipated backward doubly stochastic differential equations with integral-Lipschitz coefficients

ANAssane NdiayeUniversité Gaston Berger CGCheikh GueyeUniversité Gaston Berger SASadibou AïdaraUniversité Gaston Berger

Key Points

This research focuses on fractional delay and anticipated backward doubly stochastic differential equations, exploring their solutions.
Examined equations driven by fractional Brownian motion with Hurst parameter in (1/2, 1)
Establish existence and uniqueness of solutions for both Lipschitz and integral-Lipschitz coefficients
Utilized divergence type stochastic integrals throughout the analysis.
Demonstrated existence of solutions for fractional delay and anticipated BDSDEs under specified conditions.
Proved uniqueness of solutions in the presence of Lipschitz coefficients.
Clarified implications of the Hurst parameter on the modeling of stochastic processes.

Abstract

Abstract This paper addresses delay and anticipated backward doubly stochastic differential equations driven by fractional Brownian motion (fractional delay and anticipated BDSDEs) with Hurst parameter H ∈ (1 2, 1) H (1{2, 1) }. In these equations, the generator at time t can depend not only on the past and present but also on future solutions. We establish the existence and uniqueness of solutions in the cases of both Lipschitz and integral-Lipschitz coefficients. The stochastic integral used throughout the paper is of the divergence type.

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