Asymptotic behavior of random walks on a half-line with a jump at the origin

2011/08/29 by Guy Katriel, Katriel, Guy
Mathematics · #46N30 #47N30 #60G50 #FOS: Mathematics #Probability (math.PR) #Spectral Theory (math.SP) #math.PR #math.SP #msc:46N30 #msc:47N30 #msc:60G50

paper · pdf · doi:10.48550/arxiv.1108.5621

arxiv created 2011/08/31 · arxiv updated 2011/09/01

Abstract

We study a discrete-time random walk on the non-negative integers, such that when 0 is reached a jump occurs to an arbitrary location, with given probabilities. We obtain an asymptotic formula for the expected position at large times, in dependence on the jump probabilities and on the starting position. Our proof of this result displays the relevance of the spectral analysis of the transition operator associated to the stochastic process, both of its eigenvalues and of its resonances.

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