Wiener's test for spacetime random walks and its applications
Authors:
Yasunari Fukai and Kôhei Uchiyama
Journal:
Trans. Amer. Math. Soc. 348 (1996), 41314152
MSC (1991):
Primary 60J15, 60J45, 31C20
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Abstract: This paper establishes a criterion for whether a dimensional random walk on the integer lattice visits a spacetime 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, Meguroku, Tokyo 152, Japan
Email:
uchiyama@neptune.ap.titech.ac.jp
Kôhei Uchiyama
Affiliation:
Department of Applied Physics, Tokyo Institute of Technology, Meguroku, Tokyo 152, Japan
DOI:
http://dx.doi.org/10.1090/S0002994796016431
PII:
S 00029947(96)016431
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
