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2008 Rate of growth of a transient cookie random walk
Anne-Laure Basdevant, Arvind Singh
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Electron. J. Probab. 13: 811-851 (2008). DOI: 10.1214/EJP.v13-498

Abstract

We consider a one-dimensional transient cookie random walk. It is known from a previous paper (BS2008) that a cookie random walk $(X_n)$ has positive or zero speed according to some positive parameter $\alpha >1$ or $\leq 1$. In this article, we give the exact rate of growth of $X_n$ in the zero speed regime, namely: for $0<\alpha<1$, $X_n/n^{(α+1)/2}$ converges in law to a Mittag-Leffler distribution whereas for $\alpha=1$, $X_n(\log n)/n$ converges in probability to some positive constant.

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Anne-Laure Basdevant. Arvind Singh. "Rate of growth of a transient cookie random walk." Electron. J. Probab. 13 811 - 851, 2008. https://doi.org/10.1214/EJP.v13-498

Information

Accepted: 7 May 2008; Published: 2008
First available in Project Euclid: 1 June 2016

zbMATH: 1191.60107
MathSciNet: MR2399297
Digital Object Identifier: 10.1214/EJP.v13-498

Subjects:
Primary: 60K35
Secondary: 60F05, 60J80

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