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Recurrence properties of a special type of heavy-tailed random walk. (English) Zbl 1223.60021

Consider the heavy tail distribution

p k :=1 2ζ(3)k -3 ,k{0},

on the integer lattice and let Q=(Q n ) n=0,1,2, be the corresponding integer-valued random walk. Furthermore, let S=(S n ) n=0,1,2, be the random walk on the two-dimensional integer lattice with step distribution

p (0,k) ' =p (k,0) ' =1 2p k ·

The author derives local limit theorems for Q and S as well as the asymptotics for the time of first return to the origin, and the number of visits to the origin in the first n steps.

MSC:
60F05Central limit and other weak theorems
60G50Sums of independent random variables; random walks
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