Hitting time of a half-line by a two-dimensional nonsymmetric random walk

2012/12/12 by Yasunari Fukai, Fukai, Yasunari
Mathematics · Physics and Astronomy · #Scientific Research and Discoveries #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60E10 #msc:60G50

paper · pdf · doi:10.48550/arxiv.1212.2714

arxiv created 2012/12/12 · arxiv updated 2012/12/13

Abstract

We consider the probability that a two-dimensional random walk starting from the origin never returns to the half-line (- ∞,0] × 0 before time n. Let X⁽¹⁾=(X₁,X₂) be the increment of the two-dimensional random walk. For an aperiodic random walk with moment conditions (E[X₂]=0 and E[|X₁|^δ]<∞, E[|X₂|^{2+ δ}]< ∞ for some δ∈ (0,1)), we obtain an asymptotic estimate (as n → ∞ ) of this probability by assuming the behavior of the characteristic function of X₁ near zero.

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