Mean-field reflected backward stochastic differential equations
In this paper, mean-field reflected backward stochastic differential equations (MF-RBSDEs, for short) are introduced and studied. We prove the existence and uniqueness of solutions for MF-RBSDEs under the Lipschitz condition by a fixed point argument. Under monotone assumptions for coefficients, we show a comparison theorem for MF-RBSDEs. We finally get an existence and a comparison theorem of the minimal solution when the coefficients are continuous, non-decreasing in y′ and have a linear growth.
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Volume (Year): 82 (2012)
Issue (Month): 11 ()
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- Ahmed, N. U. & Ding, X., 1995. "A semilinear Mckean-Vlasov stochastic evolution equation in Hilbert space," Stochastic Processes and their Applications, Elsevier, vol. 60(1), pages 65-85, November.
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