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Mean-field reflected backward stochastic differential equations

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  • Li, Zhi
  • Luo, Jiaowan
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    Abstract

    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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    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212002520
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 11 ()
    Pages: 1961-1968

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:11:p:1961-1968

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    Related research

    Keywords: Mean-field reflected backward stochastic differential equations; Existence and uniqueness theorem; Comparison theorem;

    References

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    1. 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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    Cited by:
    1. Zong, Gaofeng & Chen, Zengjing, 2013. "Harnack inequality for mean-field stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1424-1432.

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