| 书目名称 | Potential Functions of Random Walks in ℤ with Infinite Variance | | 副标题 | Estimates and Applic | | 编辑 | Kôhei Uchiyama | | 视频video | | | 概述 | Emphasises the significance of the potential function.Gives classical proofs of new and established results.Generalises old results to new settings | | 丛书名称 | Lecture Notes in Mathematics | | 图书封面 |  | | 描述 | .This book studies the potential functions of one-dimensional recurrent random walks on the lattice of integers with step distribution of infinite variance. The central focus is on obtaining reasonably nice estimates of the potential function. These estimates are then applied to various situations, yielding precise asymptotic results on, among other things, hitting probabilities of finite sets, overshoot distributions, Green functions on long finite intervals and the half-line, and absorption probabilities of two-sided exit problems..The potential function of a random walk is a central object in fluctuation theory. If the variance of the step distribution is finite, the potential function has a simple asymptotic form, which enables the theory of recurrent random walks to be described in a unified way with rather explicit formulae. On the other hand, if the variance is infinite, the potential function behaves in a wide range of ways depending on the step distribution, which the asymptotic behaviour of many functionals of the random walk closely reflects..In the case when the step distribution is attracted to a strictly stable law, aspects of the random walk have been intensively st | | 出版日期 | Book 2023 | | 关键词 | Sums of independent & identically distributed random variables; Potential theory of random walk; Rando | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-031-41020-8 | | isbn_softcover | 978-3-031-41019-2 | | isbn_ebook | 978-3-031-41020-8Series ISSN 0075-8434 Series E-ISSN 1617-9692 | | issn_series | 0075-8434 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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发表于 2025-3-21 19:26:34
