Extreme slowdowns for one-dimensional excited random walks

We study the asymptotics of the probabilities of extreme slowdown events for transient one-dimensional excited random walks. That is, if {Xn}n≥0 is a transient one-dimensional excited random walk and Tn=min{k:Xk=n}, we study the asymptotics of probabilities of the form P(Xn≤nγ) and P(Tnγ≥n) with γ<1. We show that there is an interesting change in the rate of decay of these extreme slowdown probabilities when γ<1/2.

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Year of publication:	2015
Authors:	Peterson, Jonathon
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 125.2015, 2, p. 458-481
Publisher:	Elsevier
Subject:	Excited random walk \| Large deviations

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011194114