Recurrent random walks on ℤ with infinite variance: transition probabilities of them killed on a finite set

2018/08/04 by Kôhei Uchiyama, Uchiyama, Kohei
Computer Science · Decision Sciences · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Primary 60G50 #Probability (math.PR) #Probability and Risk Models #Secondary 60J45 #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1808.01484

openalex publication_date 2018/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider an irreducible random walk on the integer lattice ℤ that is in the domain of normal attraction of a strictly stable process with index α∈ (1, 2) and obtain the asymptotic form of the distribution of the hitting time of the origin and that of the transition probability for the walk killed when it hits a finite set. The asymptotic forms obtained are valid uniformly in the natural domain of the space and time variables.

Citations

• Estimates of Potential functions of random walks on Z with zero mean and infinite variance and their applications

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