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Mathematics > Probability

arXiv:1808.01484 (math)
[Submitted on 4 Aug 2018]

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

Authors:Kohei Uchiyama
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Abstract:In this paper we consider an irreducible random walk on the integer lattice $\mathbb{Z}$ that is in the domain of normal attraction of a strictly stable process with index $\alpha\in (1, 2)$ 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.
Comments: 45 pages
Subjects: Probability (math.PR)
MSC classes: Primary 60G50, Secondary 60J45
Cite as: arXiv:1808.01484 [math.PR]
  (or arXiv:1808.01484v1 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1808.01484

Submission history

From: Kohei Uchiyama [view email]
[v1] Sat, 4 Aug 2018 13:32:35 UTC (55 KB)
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