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A revisit to -theory of super-parabolic backward stochastic partial differential equations in

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  • Du, Kai
  • Meng, Qingxin

Abstract

Backward stochastic partial differential equations of parabolic type with variable coefficients are considered in the whole Euclidean space. Improved existence and uniqueness results are given in the Sobolev space Hn () under weaker assumptions than those used by X. Zhou [X. Zhou, A duality analysis on stochastic partial differential equations, J. Funct. Anal. 103 (1992) 275-293]. As an application, a comparison theorem is obtained.

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  • 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.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:10:p:1996-2015
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    References listed on IDEAS

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    1. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    2. Ma, Jin & Yong, Jiongmin, 1997. "Adapted solution of a degenerate backward spde, with applications," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 59-84, October.
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    Cited by:

    1. 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.
    2. 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.

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