SUN Hongyan, WANG Huaming. On a Maximum of Some Random Walk on Lattice of Half Line[J]. Chinese Journal of Applied Probability and Statistics, 2023, 39(5): 633-642. DOI: 10.3969/j.issn.1001-4268.2023.05.001
Citation:
SUN Hongyan, WANG Huaming. On a Maximum of Some Random Walk on Lattice of Half Line[J]. Chinese Journal of Applied Probability and Statistics, 2023, 39(5): 633-642. DOI: 10.3969/j.issn.1001-4268.2023.05.001
SUN Hongyan, WANG Huaming. On a Maximum of Some Random Walk on Lattice of Half Line[J]. Chinese Journal of Applied Probability and Statistics, 2023, 39(5): 633-642. DOI: 10.3969/j.issn.1001-4268.2023.05.001
Citation:
SUN Hongyan, WANG Huaming. On a Maximum of Some Random Walk on Lattice of Half Line[J]. Chinese Journal of Applied Probability and Statistics, 2023, 39(5): 633-642. DOI: 10.3969/j.issn.1001-4268.2023.05.001
On a Maximum of Some Random Walk on Lattice of Half Line
Consider a nearest-neighbor random walk with certain asymptotically zero drift on the positive half line. Let M be the maximum of an excursion starting from 1 and ending at 0. We study the distribution of M and characterize its asymptotics, which is quite different from those of simple random walks.
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