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- W2068577022 abstract "We prove a relative compactness criterion in Wiener–Sobolev space which represents a natural extension of the compact embedding of Sobolev space H 1 into L 2 , at the level of random fields. Then we give a specific statement of this criterion for random fields solutions of semi-linear stochastic partial differential equations with coefficients bounded in an appropriate way. Finally, we employ this result to construct solutions for semi-linear stochastic partial differential equations with distribution as final condition. We also give a probabilistic interpretation of this solution in terms of backward doubly stochastic differential equations formulated in a weak sense." @default.
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- W2068577022 date "2004-05-01" @default.
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- W2068577022 title "A relative compactness criterion in Wiener–Sobolev spaces and application to semi-linear Stochastic PDEs" @default.
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- W2068577022 doi "https://doi.org/10.1016/s0022-1236(03)00236-2" @default.
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