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

Michael Bromberg () and Zemer Kosloff ()
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Michael Bromberg: Tel Aviv University
Zemer Kosloff: Tel Aviv University

Journal of Theoretical Probability, 2014, vol. 27, issue 2, 493-517

Abstract: Abstract Let {X n } be an integer-valued Markov chain with finite state space. Let $S_{n}=\sum_{k=0}^{n}X_{k}$ and let L n (x) be the number of times S k hits x∈ℤ 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.

Keywords: Markov chains; Brownian motion; Local times; Weak invariance principle; 60F05; 60J10; 60J55; 60J65 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10959-012-0438-z

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