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BV functions in a Gelfand triple and the stochastic reflection problem on a convex set

Zhu, X
Thursday 13 September 2012, 14:40-15:10

Seminar Room 1, Newton Institute


In this paper, we introduce a de nition of BV functions in a Gelfand triple which is an extension of the de nition of BV functions in [1] by using Dirichlet form theory. By this de nition, we can consider the stochastic re ection problem associated with a self-adjoint operator A and a cylindrical Wiener process on a convex set ?? in a Hilbert space H. We prove the existence and uniqueness of a strong solution of this problem when ?? is a regular convex set. The result is also extended to the non-symmetric case. Finally, we extend our results to the case when ?? = K , where K = ff 2 L2(0; 1)jf  ?? g;  0. 1


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