Functional laws of the iterated logarithm for local times of recurrent random walks on Z2

Endre Csáki, Pál Révész, Jay Rosen

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We prove functional laws of the iterated logarithm for L0n, the number of returns to the origin, up to step n, of recurrent random walks on Z2 with slowly varying partial Green's function. We find two distinct functional laws of the iterated logarithm depending on the scaling used. In the special case of finite variance random walks, we obtain one limit set for L0ncursive Greek chi/(log n log3 n) ; 0 ≤ cursive Greek chi ≤ 1, and a different limit set for L0cursive Greek chin/(log n log3 n) ; 0 ≤ cursive Greek chi ≤ 1. In both cases the limit sets are classes of distribution functions, with convergence in the weak topology.

Original languageEnglish
Pages (from-to)545-563
Number of pages19
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume34
Issue number4
Publication statusPublished - Jul 1998

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Functional Law of the Iterated Logarithm
Limit Set
Local Time
Random walk
Weak Topology
Green's function
Distribution Function
Scaling
Distinct
Partial
Local time

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

Functional laws of the iterated logarithm for local times of recurrent random walks on Z2. / Csáki, Endre; Révész, Pál; Rosen, Jay.

In: Annales de l'institut Henri Poincare (B) Probability and Statistics, Vol. 34, No. 4, 07.1998, p. 545-563.

Research output: Contribution to journalArticle

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