Departmental Bulletin Paper HITTING TIME OF A HALF-LINE BY A TWO-DIMENSIONAL NON-SYMMETRIC RANDOM WALK

Fukai, Yasunari

69 ( 1 )  , pp.145 - 171 , 2015-06-09 , Faculty of Mathematics, Kyushu University
ISSN:1340-6116
NCID:AA10994346
Description
We consider the probability that a two-dimensional random walk starting from the origin never returns to the half-line (−∞, 0] × {0} before time n. Let X = (X_1, X_2) be the increment of the two-dimensional random walk. For an aperiodic random walk with moment conditions E [X_2] = 0 and E [|X_1|^δ] < ∞, E [|X_2|^<2+δ>] < ∞ for some δ ∈ (0, 1), we obtain an asymptotic estimate (as n → ∞) of this probability by assuming the behavior of the characteristic function of X near zero.

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