Large and moderate deviations for the local time of a recurrent Markov chain on ℤ2

N. Gantert; O. Zeitouni

doi:10.1016/S0246-0203(98)80004-6

Large and moderate deviations for the local time of a recurrent Markov chain on ℤ²

N. Gantert
, O. Zeitouni

Technische Universität Berlin
Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

Let (X_n) be a recurrent Markov chain on ℤ² with X₀ = (0, 0) such that for some constant C, P[X_k = (0, 0)] ≤ C/k, and whose truncated Green function is slowly varying at infinity. Let L⁰_n denote the local time at zero of such a Markov chain. We prove various moderate and large deviation statements and limit laws for rescaled versions of L⁰_n, including functional versions of these. A version of Strassen's functional law of the iterated logarithm, recently discovered by E. Csáki, P. Révész and J. Rosen, can be derived as a corollary.

Original language	English
Pages (from-to)	687-704
Number of pages	18
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	34
Issue number	5
DOIs	https://doi.org/10.1016/S0246-0203(98)80004-6
State	Published - 1998
Externally published	Yes

Keywords

Large deviations
Local time
Markov chain
Strassen's law

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10.1016/S0246-0203(98)80004-6

Cite this

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title = "Large and moderate deviations for the local time of a recurrent Markov chain on ℤ2",

abstract = "Let (Xn) be a recurrent Markov chain on ℤ2 with X0 = (0, 0) such that for some constant C, P[Xk = (0, 0)] ≤ C/k, and whose truncated Green function is slowly varying at infinity. Let L0n denote the local time at zero of such a Markov chain. We prove various moderate and large deviation statements and limit laws for rescaled versions of L0n, including functional versions of these. A version of Strassen's functional law of the iterated logarithm, recently discovered by E. Cs{\'a}ki, P. R{\'e}v{\'e}sz and J. Rosen, can be derived as a corollary.",

keywords = "Large deviations, Local time, Markov chain, Strassen's law",

author = "N. Gantert and O. Zeitouni",

note = "Funding Information: AMS Class\textasciitilde{}@zrionst 60510, 60555, 60FlO. it This research was carried out while visiting the Department of Electrical Engineering. Technion Haifa, and was supported by the Swiss National Science foundation under grant 8220-0465 18. {\textquoteright} Partially supported by a US-Israel BSF grant and by grant NCR 94-225 13.",

year = "1998",

doi = "10.1016/S0246-0203(98)80004-6",

language = "English",

volume = "34",

pages = "687--704",

journal = "Annales de l'institut Henri Poincare (B) Probability and Statistics",

issn = "0246-0203",

publisher = "Institute of Mathematical Statistics",

number = "5",

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TY - JOUR

T1 - Large and moderate deviations for the local time of a recurrent Markov chain on ℤ2

AU - Gantert, N.

AU - Zeitouni, O.

N1 - Funding Information: AMS Class~@zrionst 60510, 60555, 60FlO. it This research was carried out while visiting the Department of Electrical Engineering. Technion Haifa, and was supported by the Swiss National Science foundation under grant 8220-0465 18. ’ Partially supported by a US-Israel BSF grant and by grant NCR 94-225 13.

PY - 1998

Y1 - 1998

N2 - Let (Xn) be a recurrent Markov chain on ℤ2 with X0 = (0, 0) such that for some constant C, P[Xk = (0, 0)] ≤ C/k, and whose truncated Green function is slowly varying at infinity. Let L0n denote the local time at zero of such a Markov chain. We prove various moderate and large deviation statements and limit laws for rescaled versions of L0n, including functional versions of these. A version of Strassen's functional law of the iterated logarithm, recently discovered by E. Csáki, P. Révész and J. Rosen, can be derived as a corollary.

AB - Let (Xn) be a recurrent Markov chain on ℤ2 with X0 = (0, 0) such that for some constant C, P[Xk = (0, 0)] ≤ C/k, and whose truncated Green function is slowly varying at infinity. Let L0n denote the local time at zero of such a Markov chain. We prove various moderate and large deviation statements and limit laws for rescaled versions of L0n, including functional versions of these. A version of Strassen's functional law of the iterated logarithm, recently discovered by E. Csáki, P. Révész and J. Rosen, can be derived as a corollary.

KW - Large deviations

KW - Local time

KW - Markov chain

KW - Strassen's law

UR - https://www.scopus.com/pages/publications/0032163552

U2 - 10.1016/S0246-0203(98)80004-6

DO - 10.1016/S0246-0203(98)80004-6

M3 - Article

AN - SCOPUS:0032163552

SN - 0246-0203

VL - 34

SP - 687

EP - 704

JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

IS - 5

ER -

Large and moderate deviations for the local time of a recurrent Markov chain on ℤ²

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Keywords

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