Electronic Communications in Probability

On Recurrent and Transient Sets of Inhomogeneous Symmetric Random Walks

Giambattista Giacomin and Gustavo Posta

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Abstract

We consider a continuous time random walk on the $d$-dimensional lattice $\mathbb{Z}^d$: the jump rates are time dependent, but symmetric and strongly elliptic with ellipticity constants independent of time. We investigate the implications  of heat kernel estimates on recurrence-transience  properties of the walk and we give conditions for recurrence as well as for transience: we give applications of these conditions  and discuss them in relation with the (optimal) Wiener test available in the time independent context. Our approach relies on estimates on the time spent by the walk in a set and on a 0-1 law. We show also that, still via heat kernel estimates, one can avoid using a 0-1 law, achieving this way quantitative estimates on more general hitting probabilities.

Article information

Source
Electron. Commun. Probab., Volume 6 (2001), paper no. 4, 39-53.

Dates
Accepted: 18 January 2001
First available in Project Euclid: 19 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1461097549

Digital Object Identifier
doi:10.1214/ECP.v6-1033

Mathematical Reviews number (MathSciNet)
MR1831800

Zentralblatt MATH identifier
0976.60073

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60J75: Jump processes 82B41: Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41]

Keywords
Inhomogeneous Symmetric Random Walks Heat Kernel Estimates Recurrence-Transience Hitting Probabilities Wiener test Paley-Zygmund inequality

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Giacomin, Giambattista; Posta, Gustavo. On Recurrent and Transient Sets of Inhomogeneous Symmetric Random Walks. Electron. Commun. Probab. 6 (2001), paper no. 4, 39--53. doi:10.1214/ECP.v6-1033. https://projecteuclid.org/euclid.ecp/1461097549


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