TY - JOUR
T1 - Weak Invariance Principle for the Local Times of Partial Sums of Markov Chains
AU - Bromberg, Michael
AU - Kosloff, Zemer
PY - 2014/6
Y1 - 2014/6
N2 - 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.
AB - 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.
KW - Brownian motion
KW - Local times
KW - Markov chains
KW - Weak invariance principle
UR - http://www.scopus.com/inward/record.url?scp=84899563282&partnerID=8YFLogxK
U2 - 10.1007/s10959-012-0438-z
DO - 10.1007/s10959-012-0438-z
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AN - SCOPUS:84899563282
SN - 0894-9840
VL - 27
SP - 493
EP - 517
JO - Journal of Theoretical Probability
JF - Journal of Theoretical Probability
IS - 2
ER -