Global limit theorems on the convergence of multidimensional random walks to stable processes

A. Agbor; S. Molchanov; B. Vainberg

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arXiv · 1405.2487

Global limit theorems on the convergence of multidimensional random walks to stable processes

A. Agbor·S. Molchanov·B. Vainberg

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Abstract

Symmetric heavily tailed random walks on $Z^d, d\geq 1,$ are considered. Under appropriate regularity conditions on the tails of the jump distributions, global (i.e., uniform in $x,t, |x|+t\to\infty,$) asymptotic behavior of the transition probability $p(t,0,x)$ is obtained. The examples indicate that the regularity conditions are essential.

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BibTeX RIS

A. Agbor, S. Molchanov, B. Vainberg. 2014-05-11. Global limit theorems on the convergence of multidimensional random walks to stable processes. https://arxiv.org/abs/1405.2487

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