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Reflected backward stochastic partial differential equations in a convex domain

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  • Yang, Xue
  • Zhang, Qi
  • Zhang, Tusheng

Abstract

This paper is concerned with the reflected backward stochastic partial differential equations, taking values in a convex domain in Rk. The existence and uniqueness of solution are studied under both the super-parabolic and parabolic conditions. In the degenerate parabolic case the connection between reflected backward stochastic partial differential equations and reflected forward backward stochastic differential equations is established.

Suggested Citation

  • Yang, Xue & Zhang, Qi & Zhang, Tusheng, 2020. "Reflected backward stochastic partial differential equations in a convex domain," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6038-6063.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:10:p:6038-6063
    DOI: 10.1016/j.spa.2020.05.002
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    References listed on IDEAS

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    1. Bernt Øksendal & Agnès Sulem & Tusheng Zhang, 2014. "Singular Control and Optimal Stopping of SPDEs, and Backward SPDEs with Reflection," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 464-486, May.
    2. Matoussi, Anis & Sabbagh, Wissal & Zhang, Tusheng, 2017. "Backward doubly SDEs and semilinear stochastic PDEs in a convex domain," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 2781-2815.
    3. Yang, Xue, 2019. "Reflected backward stochastic partial differential equations with jumps in a convex domain," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 126-136.
    4. Ma, Jin & Yin, Hong & Zhang, Jianfeng, 2012. "On non-Markovian forward–backward SDEs and backward stochastic PDEs," Stochastic Processes and their Applications, Elsevier, vol. 122(12), pages 3980-4004.
    5. Xu, Tiange & Zhang, Tusheng, 2009. "White noise driven SPDEs with reflection: Existence, uniqueness and large deviation principles," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3453-3470, October.
    6. Du, Kai & Zhang, Qi, 2013. "Semi-linear degenerate backward stochastic partial differential equations and associated forward–backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1616-1637.
    7. Zhang, Tusheng, 2011. "Systems of stochastic partial differential equations with reflection: Existence and uniqueness," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1356-1372, June.
    8. Du, Kai & Meng, Qingxin, 2010. "A revisit to -theory of super-parabolic backward stochastic partial differential equations in," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 1996-2015, September.
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