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Existence and uniqueness of solutions for BDSDEs with weak monotonicity coefficients

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  • Zhu, Runyu
  • Tian, Dejian

Abstract

In this paper, we study backward doubly stochastic differential equations (BDSDEs for short) with weak monotonicity coefficients. With the help of choosing the suitable approximation sequence, we derive the existence and uniqueness of solutions to BDSDEs. The comparison theorem is also established in one-dimensional situation.

Suggested Citation

  • Zhu, Runyu & Tian, Dejian, 2019. "Existence and uniqueness of solutions for BDSDEs with weak monotonicity coefficients," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 48-55.
    • Handle: RePEc:eee:stapro:v:153:y:2019:i:c:p:48-55
    DOI: 10.1016/j.spl.2019.05.017
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    References listed on IDEAS

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    1. Briand, Ph. & Delyon, B. & Hu, Y. & Pardoux, E. & Stoica, L., 2003. "Lp solutions of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 109-129, November.
    2. Lepeltier, J. P. & San Martin, J., 1997. "Backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 425-430, April.
    3. Lin, Qian, 2009. "A class of backward doubly stochastic differential equations with non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2223-2229, October.
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