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- W1586410513 abstract "This paper presents existence and uniqueness results for reflected backward doubly stochastic differential equations (in short RBDDSEs) in a convex domain D. Moreover, using a stochastic flow approach a probabilistic interpretation for a class of reflected SPDE's in a domain is given via such RBDSDEs. The solution is expressed as a pair (u,{nu}) where u is a predictable continuous process which takes values in a Sobolev space and m is a random regular measure. The bounded variation process K, component of the solution of the reflected BDSDE, controls the set when u reaches the boundary of D. This bounded variation process determines the measure m from a particular relation by using the inverse of the flow associated to the the diffusion operator." @default.
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- W1586410513 date "2014-05-22" @default.
- W1586410513 modified "2023-09-24" @default.
- W1586410513 title "Backward Doubly SDEs and Semilinear Stochastic PDEs in a convex domain" @default.
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- W1586410513 doi "https://doi.org/10.48550/arxiv.1405.5822" @default.
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