期刊
JOURNAL OF THEORETICAL PROBABILITY
卷 29, 期 4, 页码 1685-1709出版社
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10959-015-0626-8
关键词
Random walk on a spider; Brownian spider; Transition probabilities; Strong approximations; Laws of the iterated logarithm; Brownian and random walk heights on spider
资金
- Hungarian National Foundation for Scientific Research [K108615]
- NSERC Canada Discovery Grant at Carleton University
- PSC CUNY [68030-0043]
A simple random walk is considered on a spider that is a collection of half lines (we call them legs) joined at the origin. We establish a strong approximation of this random walk by the so-called Brownian spider. Transition probabilities are studied, and for a fixed number of legs we investigate how high the walker and the Brownian motion can go on the legs in n steps. The heights on the legs are also investigated when the number of legs goes to infinity.
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