White noise driven SPDEs with reflection: Existence, uniqueness and large deviation principles
By Tiange Xu, Tusheng Zhang. 2009
97 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Finance
View Paper: https://www.semanticscholar.org/paper/aa30fd53bc91106d3bf01f7bd72962ac82d63505
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In Computational Theory and Mathematics
In Control and Systems Engineering
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Citations in the corpus
- White Noise Driven SPDEs with Reflection: Strong Feller Properties and Harnack Inequalities (2010, background): “2 It has been newly proved in [13] that the minimal solution of Eq.”