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L p Theory for Super-Parabolic Backward Stochastic Partial Differential Equations in the Whole Space

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Abstract

This paper is concerned with semi-linear backward stochastic partial differential equations (BSPDEs for short) of super-parabolic type. An L p-theory is given for the Cauchy problem of BSPDEs, separately for the case of p∈(1,2] and for the case of p∈(2,∞). A comparison theorem is also addressed.

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Authors and Affiliations

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

    Kai Du, Jinniao Qiu & 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. Jinniao Qiu
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  3. Shanjian Tang
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Corresponding author

Correspondence to Jinniao Qiu.

Additional information

Communicating Editor: Alain Bensoussan.

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, 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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Du, K., Qiu, J. & Tang, S. L p Theory for Super-Parabolic Backward Stochastic Partial Differential Equations in the Whole Space. Appl Math Optim 65, 175–219 (2012). https://doi.org/10.1007/s00245-011-9154-9

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