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.
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Received: 24 September 1997 / Revised version: 3 June 1998
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Ma, J., Yong, J. On linear, degenerate backward stochastic partial differential equations. Probab Theory Relat Fields 113, 135–170 (1999). https://doi.org/10.1007/s004400050205
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DOI: https://doi.org/10.1007/s004400050205
- Mathematics Subject Classification (1991): 60H15, 35R60, 34F05, 93E20
- Key words: Degenerate backward stochastic partial differential equations, adapted solutions, comparison theorems