Asymptotically stable random walks of index 1<α<2 killed on a finite set

Kôhei Uchiyama

Stochastic Processes and their Applications, 2019, vol. 129, issue 12, 5151-5199

Abstract: For a random walk on the integer lattice Z that is attracted to a strictly stable process with index α∈(1,2) we obtain the asymptotic form of the transition probability for the walk killed when it hits a finite set. The asymptotic forms obtained are valid uniformly in a natural range of the space and time variables. The situation is relatively simple when the limit stable process has jumps in both positive and negative directions; in the other case when the jumps are one sided rather interesting matters are involved and detailed analyses are necessitated.

Keywords: One dimensional random walk; First passage time; Killed at the origin; In a domain of attraction; Transition probability; Stable process (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spa.2019.02.006

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