White noise driven SPDEs with reflection: Existence,uniqueness and large deviation principles |
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Authors: | Tiange Xu Tusheng Zhang |
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Affiliation: | 1. School of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, England, UK;2. CMA, University of Oslo, P.O.Box 1053, Blindern, 0316 Oslo, Norway |
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Abstract: | In the first part of this paper, we prove the uniqueness of the solutions of SPDEs with reflection, which was left open in the paper [C. Donati-Martin, E. Pardoux, White noise driven SPDEs with reflection, Probab. Theory Related Fields 95 (1993) 1–24]. We also obtain the existence of the solution for more general coefficients depending on the past with a much shorter proof. In the second part of the paper, we establish a large deviation principle for SPDEs with reflection. The weak convergence approach is proven to be very efficient on this occasion. |
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Keywords: | primary, 60H15 secondary, 60F10, 60F05 |
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