### 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

#### Abstract

In this paper, we introduce a denition of BV functions in a Gelfand triple which is an
extension of the denition of BV functions in [1] by using Dirichlet form theory. By this
denition, 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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