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Wiener's test for space-time random walks and its applications |
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| Authors: | Yasunari Fukai Kô hei Uchiyama |
| Affiliation: | Department of Applied Physics, Tokyo Institute of Technology, Meguro-ku, Tokyo 152, Japan ; Department of Applied Physics, Tokyo Institute of Technology, Meguro-ku, Tokyo 152, Japan |
| 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. |
| Keywords: | Wiener's test random walk Kolmogorov's test discrete heat equation regularity of a minimal Martin boundary point |
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