In this paper we prove two relatively compact criterions in some Lp-spaces(p > 1) for the set of functionals on abstract Wiener space in terms of the compact embedding theorems in finite dimensional Sobolev spaces. Then, as applications we study several relatively compact families of random fields for the solutions to SDEs (and SPDEs) with coefficients satisfying some bounded assumptions, some stochastic integrals, and local times of diffusion processes. © 2005 Elsevier Inc. All rights reserved.
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