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Probability Theory and Related Fields

, Volume 113, Issue 2, pp 135–170 | Cite as

On linear, degenerate backward stochastic partial differential equations

  • Jin Ma
  • Jiongmin Yong

Abstract.

In this paper we study the well-posedness and regularity of the adapted solutions to a class of linear, degenerate backward stochastic partial differential equations (BSPDE, for short). We establish new a priori estimates for the adapted solutions to BSPDEs in a general setting, based on which the existence, uniqueness, and regularity of adapted solutions are obtained. Also, we prove some comparison theorems and discuss their possible applications in mathematical finance.

Mathematics Subject Classification (1991): 60H15, 35R60, 34F05, 93E20 
Key words: Degenerate backward stochastic partial differential equations, adapted solutions, comparison theorems 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Jin Ma
    • 1
  • Jiongmin Yong
    • 2
  1. 1.Department of Mathematics, Purdue University, West Lafayette, IN 47907-1395, USA. e-mail: majin@math.purdue.eduUS
  2. 2.Laboratory of Mathematics for Nonlinear Sciences and Department of Mathematics, Fudan University, Shanghai 200433, China.CN

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