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Reflected backward stochastic partial differential equations in a convex domain. (English) Zbl 07243113
Summary: This paper is concerned with the reflected backward stochastic partial differential equations, taking values in a convex domain in $$\mathbb{R}^k$$. The existence and uniqueness of solution are studied under both the super-parabolic and parabolic conditions. In the degenerate parabolic case the connection between reflected backward stochastic partial differential equations and reflected forward backward stochastic differential equations is established.
MSC:
 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 60G46 Martingales and classical analysis 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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