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On semi-linear degenerate backward stochastic partial differential equations
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  • Published: July 2002

On semi-linear degenerate backward stochastic partial differential equations

  • Ying Hu1,
  • Jin Ma2 &
  • Jiongmin Yong3 

Probability Theory and Related Fields volume 123, pages 381–411 (2002)Cite this article

  • 325 Accesses

  • 60 Citations

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Abstract.

 In this paper we study a class of one-dimensional, degenerate, semilinear backward stochastic partial differential equations (BSPDEs, for short) of parabolic type. By establishing some new a priori estimates for both linear and semilinear BSPDEs, we show that the regularity and uniform boundedness of the adapted solution to the semilinear BSPDE can be determined by those of the coefficients, a special feature that one usually does not expect from a stochastic differential equation. The proof follows the idea of the so-called bootstrap method, which enables us to analyze each of the derivatives of the solution under consideration. Some related results, including some comparison theorems of the adapted solutions for semilinear BSPDEs, as well as a nonlinear stochastic Feynman-Kac formula, are also given.

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Authors and Affiliations

  1. IRMAR, U.M.R. C.N.R.S. 6625, Campus de Beaulieu, Université Rennes 1, 35042 Rennes Cedex, France. e-mail: hu@maths.univ-rennes1.fr, , , , , , FR

    Ying Hu

  2. Department of Mathematics, Purdue University, West Lafayette, IN 47907-1395. This author is supported in part by National Science Foundation grant &#;DMS 9970710., , , , ,

    Jin Ma

  3. Laboratory of Mathematics for Nonlinear Sciences, Department of Mathematics, and Institute of Mathematical Finance, Fudan University, Shanghai 200433, China., , , , , , CN

    Jiongmin Yong

Authors
  1. Ying Hu
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  2. Jin Ma
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  3. Jiongmin Yong
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Additional information

Received: 16 January 2001 / Revised version: 11 October 2001 / Published online: 14 June 2002

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Hu, Y., Ma, J. & Yong, J. On semi-linear degenerate backward stochastic partial differential equations. Probab Theory Relat Fields 123, 381–411 (2002). https://doi.org/10.1007/s004400100193

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  • Issue Date: July 2002

  • DOI: https://doi.org/10.1007/s004400100193

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Stochastic Differential Equation
  • Related Result
  • Bootstrap Method
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