Weak convergence of diffusion processes on Wiener space

• 成果类型: Article
• 署名作者: Kolesnikov, Alexander V.
• 署名单位: Scuola Normale Superiore di Pisa
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-006-0023-4
• 发表日期: 2008
• 页码: 1-17
• 关键词: generalized schrodinger-operators; dirichlet forms; infinite dimensions; mosco-convergence; uniqueness; EQUATIONS; limit

摘要

Let gamma be a Gaussian measure on a Suslin space X, H be the corresponding Cameron-Martin space and {e (i) } subset of H be an orthonormal basis of H. Suppose that mu (n) = rho (n) center dot gamma is a sequence of probability measures which converges weakly to a probability measure mu = rho center dot gamma Consider a sequence of Dirichlet forms {E-n}, where E-n (f) = integral(x) parallel to del Hf parallel to(2)(H)p(n) d gamma and root p(n) epsilon W-2,W-1(gamma).We prove some sufficient conditions for Mosco convergence.