SOME ZERO-ONE LAWS FOR ADDITIVE-FUNCTIONALS OF MARKOV-PROCESSES

• 成果类型: Article
• 署名作者: HOHNLE, R; STURM, KT
• 署名单位: University of Erlangen Nuremberg
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/BF01268986
• 发表日期: 1994
• 页码: 407-416
• 关键词: bessel

摘要

Let (X(t), P-x) be an m-symmetric Markov process with a strictly transition density. Consider the additive functional A(t):= integral(0)(t)f(X(s)) (is where f: E --> [0, infinity] is a universally measurable function on the state space E. Among others, we prove that P-x(A(t) < infinity) = 1, for some x is an element of EE and some t > 0, already implies P-x(A(t) < infinity) = 1, for quasi every x is an element of E and all t > 0. The latter is also equivalent to P-x(A(t) < infinity) > 0, for quasi every x is an element of E and all t > 0, and to the analytic condition integral(Fn)fdm < infinity, for a sequence of finely open Borel sets F-n such that E\boolean OR F-n is polar. In the special cases of Brownian motion and Bessel process, these results were obtained earlier by H.J. Engelbert, W. Schmidt, X.-X. Xue and the authors.