In this paper we prove the existence of a solution for mean-field reflected backward doubly stochastic differential equations (MF-RBDSDEs) with one continuous barrier and discontinuous generator (left-continuous). By a comparison theorem establish here for MF-RBDSDEs, we provide a minimal or a maximal solution to MF-RBDSDEs.
In this work, we will try to weaken the hypothesis imposed by Hu and Peng. We will be concerned with finding the solution of locally monotone BSDEs associated to fBm. As an auxiliary
step, we study the existence and uniqueness of a solution to the monotone
backward SDEs associated to fBm. Then we connect these two kinds of
fractional backward SDEs with the corresponding semilinear partial differential equations (PDEs for short).
In this paper, we deal with the fractional backward stochastic differential equations (F-BSDEs in short) with Hurst parameter $H\in (\frac{1}{2},1)$ when the driver $g$ is weak monotone. Via an approximation theory, we derive the existence and uniqueness of solutions to F-BSDEs. The comparison theorem is also established.
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