On occupation time functionals for diffusion processes and birth-and-death processes on graphs

• 成果类型: Article
• 署名作者: Weber, M
• 署名单位: Technische Universitat Dresden
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2001
• 页码: 544-567
• 关键词: random perturbations

摘要

Occupation time functionals for a diffusion process or a birth-and-death process on the edges of a graph Gamma depending only on the values of the process on a part Gamma ' subset of Gamma of Gamma are closely related to so-called eigenvalue depending boundary conditions for the resolvent of the process. Under the assumption that the connected components of Gamma \ Gamma ' are trees, we use the special structure of these boundary conditions to give a procedure that replaces each of the trees by only one edge and that associates this edge with a speed measure such that the respective functional for the appearing process on the simplified graph coincides with the original one.