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Strong solution of backward stochastic partial differential equations in C 2 domains
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  • Published: 01 June 2011

Strong solution of backward stochastic partial differential equations in C 2 domains

  • Kai Du1 &
  • Shanjian Tang1,2 

Probability Theory and Related Fields volume 154, pages 255–285 (2012)Cite this article

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  • 30 Citations

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Abstract

This paper is concerned with the strong solution to the Cauchy–Dirichlet problem for backward stochastic partial differential equations of parabolic type. Existence and uniqueness theorems are obtained, due to an application of the continuation method under fairly weak conditions on variable coefficients and C 2 domains. The problem is also considered in weighted Sobolev spaces which allow the derivatives of the solutions to blow up near the boundary. As applications, a comparison theorem is obtained and the semi-linear equation is discussed in the C 2 domain.

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Author information

Authors and Affiliations

  1. Department of Finance and Control Sciences, School of Mathematical Sciences and Laboratory of Mathematics for Nonlinear Science, Fudan University, Shanghai, 200433, China

    Kai Du & Shanjian Tang

  2. Graduate Department of Financial Engineering, Ajou University, San 5, Woncheon-dong, Yeongtong-gu, Suwon, 443-749, Korea

    Shanjian Tang

Authors
  1. Kai Du
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  2. Shanjian Tang
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Corresponding author

Correspondence to Shanjian Tang.

Additional information

Supported by NSFC Grant #10325101, by Basic Research Program of China (973 Program) Grant # 2007CB814904, by the Science Foundation of the Ministry of Education of China Grant #200900071110001, by Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT) (NO. IRT0912), and by WCU (World Class University) Program through the Korea Science and Engineering Foundation funded by the Ministry of Education, Science and Technology (R31-2009-000-20007).

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Cite this article

Du, K., Tang, S. Strong solution of backward stochastic partial differential equations in C 2 domains. Probab. Theory Relat. Fields 154, 255–285 (2012). https://doi.org/10.1007/s00440-011-0369-0

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  • Received: 11 June 2010

  • Revised: 18 February 2011

  • Published: 01 June 2011

  • Issue Date: October 2012

  • DOI: https://doi.org/10.1007/s00440-011-0369-0

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Keywords

  • Backward stochastic partial differential equations
  • Strong solutions
  • C 2 domains
  • Weighted Sobolev spaces

Mathematics Subject Classification (2000)

  • 60H15
  • 35R60
  • 93E20
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