Stochastic processes and their applications, 2005-09, Vol.115 (9), p.1503-1517
2005
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Details
- Autor(en) / Beteiligte
- Titel
- Frequently visited sets for random walks
- Ist Teil von
- Stochastic processes and their applications, 2005-09, Vol.115 (9), p.1503-1517
- Ort / Verlag
- Amsterdam: Elsevier B.V
- Erscheinungsjahr
- 2005
- Quelle
- Alma/SFX Local Collection
- Beschreibungen/Notizen
- We study the occupation measure of various sets for a symmetric transient random walk in Z d with finite variances. Let μ n X ( A ) denote the occupation time of the set A up to time n. It is shown that sup x ∈ Z d μ n X ( x + A ) / log n tends to a finite limit as n → ∞ . The limit is expressed in terms of the largest eigenvalue of a matrix involving the Green function of X restricted to the set A. Some examples are discussed and the connection to similar results for Brownian motion is given.
- Sprache
- Englisch
- Identifikatoren
- ISSN: 0304-4149eISSN: 1879-209XDOI: 10.1016/j.spa.2005.04.003Titel-ID: cdi_hal_primary_oai_HAL_hal_00101839v1
- Format
- –
- Schlagworte
- Exact sciences and technology, Limit theorems, Markov processes, Mathematics, Occupation measure, Probability, Probability and statistics, Probability theory and stochastic processes, Random walk, Random walk Occupation measure Strong theorems, Sciences and techniques of general use, Stochastic processes, Strong theorems