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	THE STOCHASTIC REFLECTION PROBLEM ON AN INFINITE DIMENSIONAL CONVEX SET AND BV FUNCTIONS IN A GELFAND TRIPLE
	Roeckner, Michael ; Zhu, Rong-Chan ; Zhu, Xiang-Chan
	2012
关键词	Dirichlet forms stochastic reflection problems BV function Gelfand triples integration by parts formula in infinite dimensions EQUATIONS SPACE THEOREM SPDES
英文摘要	In this paper, we introduce a definition of BV functions in a Gelfand triple which is an extension of the definition of BV functions in [Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur Rend. Lincei (9) Mat. Appl. 21 (2010) 405-414] by using Dirichlet form theory. By this definition, we can consider the stochastic reflection problem associated with a self-adjoint operator A and a cylindrical Wiener process on a convex set Gamma in a Hilbert space H. We prove the existence and uniqueness of a strong solution of this problem when Gamma is a regular convex set. The result is also extended to the nonsymmetric case. Finally, we extend our results to the case when Gamma = K-alpha, where K-alpha = {f is an element of L-2(0, 1)vertical bar f >= -alpha), alpha > 0.; Statistics & Probability; SCI(E); 2; ARTICLE; 4; 1759-1794; 40
语种	英语
出处	SCI
出版者	annals of probability
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/393157]
专题	数学科学学院
推荐引用方式 GB/T 7714	Roeckner, Michael,Zhu, Rong-Chan,Zhu, Xiang-Chan. THE STOCHASTIC REFLECTION PROBLEM ON AN INFINITE DIMENSIONAL CONVEX SET AND BV FUNCTIONS IN A GELFAND TRIPLE. 2012-01-01.

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