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

Michael Bromberg, Zemer Kosloff*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Let {Xn} be an integer-valued Markov chain with finite state space. Let Sn = Σk=0n Xk and let Ln(x) be the number of times Sk hits x ∈ ℤ up to step n. Define the normalized local time process ln(t,x) by (Formula presented.). The subject of this paper is to prove a functional weak invariance principle for the normalized sequence ln(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.

Original languageAmerican English
Pages (from-to)493-517
Number of pages25
JournalJournal of Theoretical Probability
Volume27
Issue number2
DOIs
StatePublished - Jun 2014
Externally publishedYes

Keywords

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

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