A Ray-Knight theorem for symmetric Markov processes

• 成果类型: Article
• 署名作者: Eisenbaum, N; Kaspi, H; Marcus, MB; Rosen, J; Shi, Z
• 署名单位: Sorbonne Universite; City University of New York (CUNY) System; City College of New York (CUNY); Technion Israel Institute of Technology; City University of New York (CUNY) System; College of Staten Island (CUNY)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2000
• 页码: 1781-1796
• 关键词: sample path properties; additive-functionals

摘要

Let X be a strongly symmetric recurrent Markov process with state space S and let L-t(x) denote the local time of X at x is an element of S. For a fixed element 0 in the state space S, let tau (t) := inf{s: L-s(0) > t}. The 0-potential density, u({o})(x, y), of the process X killed at T-0 = inf{s: X-s = 0), is symmetric and positive definite. Let eta = {eta (x); x is an element of S} be a mean-zero Gaussian process with covariance E-eta(eta (x)eta (y)) = u({0})(x, y). The main result of this paper is the following generalization of the classical second Ray-Knight theorem: for any b is an element of R and t > 0, {L-r(t)(x) + 1/2(eta (x) + b)(2); x is an element of S} = {1/2(eta (x) + root 2t + b(2))(2); x is an element of S} in law. A version of this theorem is also given when X is transient.