Uniqueness of Nelson's diffusions

• 成果类型: Article
• 署名作者: Wu, LM
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite Clermont Auvergne (UCA)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• 发表日期: 1999
• 页码: 549-585
• 关键词: generalized schrodinger-operators; essential self-adjointness; EXTENSIONS; mechanics

摘要

Let L := Delta/2 + (del phi/phi) . del be a generalized Schrodinger operator or generator of Nelson's diffusion, defined on C-0(infinity)(D) where phi is a continuous and strictly positive function on an open domain D subset of R-d such that del phi is an element of L-loc(2)(D). Some results are given about the two questions below: (i) Whether does L generate a unique semigroup in L-1(D, phi(2) dx)? (ii) Whether the semigroup determined by L is strong Feller?