Wiener's test for space-time random walks

and its applications

Authors:
Yasunari Fukai and Kôhei Uchiyama

Journal:
Trans. Amer. Math. Soc. **348** (1996), 4131-4152

MSC (1991):
Primary 60J15, 60J45, 31C20

DOI:
https://doi.org/10.1090/S0002-9947-96-01643-1

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper establishes a criterion for whether a -dimensional random walk on the integer lattice visits a space-time subset infinitely often or not. It is a precise analogue of Wiener's test for regularity of a boundary point with respect to the classical Dirichlet problem. The test obtained is applied to strengthen the harder half of Kolmogorov's test for the random walk.

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Additional Information

**Yasunari Fukai**

Affiliation:
Department of Applied Physics, Tokyo Institute of Technology, Meguro-ku, Tokyo 152, Japan

Email:
uchiyama@neptune.ap.titech.ac.jp

**Kôhei Uchiyama**

Affiliation:
Department of Applied Physics, Tokyo Institute of Technology, Meguro-ku, Tokyo 152, Japan

DOI:
https://doi.org/10.1090/S0002-9947-96-01643-1

Keywords:
Wiener's test,
random walk,
Kolmogorov's test,
discrete heat equation,
regularity of a minimal Martin boundary point

Received by editor(s):
May 10, 1995

Article copyright:
© Copyright 1996
American Mathematical Society