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2014 Localization for controlled random walks and martingales
Ori Gurel-Gurevich, Yuval Peres, Ofer Zeitouni
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Electron. Commun. Probab. 19: 1-8 (2014). DOI: 10.1214/ECP.v19-3081

Abstract

We consider controlled random walks that are martingales with uniformly bounded increments and nontrivial jump probabilities and show that such walks can be constructed so that $P(S_n^u=0)$ decays at polynomial rate $n^{-\alpha}$ where $\alpha>0$ can be arbitrarily small. We also show, by means of a general delocalization lemma for martingales, which is of independent interest, that slower than polynomial decay is not possible.

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Ori Gurel-Gurevich. Yuval Peres. Ofer Zeitouni. "Localization for controlled random walks and martingales." Electron. Commun. Probab. 19 1 - 8, 2014. https://doi.org/10.1214/ECP.v19-3081

Information

Accepted: 26 April 2014; Published: 2014
First available in Project Euclid: 7 June 2016

zbMATH: 1312.60053
MathSciNet: MR3208322
Digital Object Identifier: 10.1214/ECP.v19-3081

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