Recurrent random walks on $\mathbb{Z}$ with infinite variance: transition probabilities of them killed on a finite set
Kohei Uchiyama
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.
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