Extreme slowdowns for one-dimensional excited random walks

Jonathon Peterson

Stochastic Processes and their Applications, 2015, vol. 125, issue 2, 458-481

Abstract: 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.

Keywords: Excited random walk; Large deviations (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spa.2014.09.017

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