Weak Invariance Principle for the Local Times of Partial Sums of Markov Chains

作者：Bromberg Michael; Kosloff Zemer^*

来源：Journal of Theoretical Probability, 2014, 27(2): 493-517.

DOI：10.1007/s10959-012-0438-z

• Markov chains
• Brownian motion
• Local times
• Weak invariance principle

Let {X (n) } be an integer-valued Markov chain with finite state space. Let and let L (n) (x) be the number of times S (k) hits xaa"currency sign up to step n. Define the normalized local time process l (n) (t,x) by The subject of this paper is to prove a functional weak invariance principle for the normalized sequence l (n) (t,x), i.e., we prove under the assumption of strong aperiodicity of the Markov chain that the normalized local times converge in distribution to the local time of the Brownian motion.

• 出版日期2014-6