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Titlebook: Stopped Random Walks; Limit Theorems and A Allan Gut Textbook 2009Latest edition Springer-Verlag New York 2009 Probability theory.Sage.limi

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发表于 2025-3-21 17:24:11 | 显示全部楼层 |阅读模式
书目名称Stopped Random Walks
副标题Limit Theorems and A
编辑Allan Gut
视频video
概述Second edition features a new chapter on perturbed random walks, which are modeled as random walks plus “noise”.Presents updates to the first edition, including an outlook on further results, extensio
丛书名称Springer Series in Operations Research and Financial Engineering
图书封面Titlebook: Stopped Random Walks; Limit Theorems and A Allan Gut Textbook 2009Latest edition Springer-Verlag New York 2009 Probability theory.Sage.limi
描述.Classical probability theory provides information about random walks after a fixed number of steps. For applications, however, it is more natural to consider random walks evaluated after a .random. number of steps. Examples are sequential analysis, queueing theory, storage and inventory theory, insurance risk theory, reliability theory, and the theory of counters. .Stopped Random Walks: Limit Theorems and Applications .shows how this theory can be used to prove limit theorems for renewal counting processes, first passage time processes, and certain two-dimensional random walks, and to how these results are useful in various applications...This second edition offers updated content and an outlook on further results, extensions and generalizations. A new chapter examines nonlinear renewal processes in order to present the analagous theory for perturbed random walks, modeled as a random walk plus “noise”..
出版日期Textbook 2009Latest edition
关键词Probability theory; Sage; limit theorems; perturbed random walks; probability; renewal processes; two-dime
版次2
doihttps://doi.org/10.1007/978-0-387-87835-5
isbn_softcover978-1-4419-2773-6
isbn_ebook978-0-387-87835-5Series ISSN 1431-8598 Series E-ISSN 2197-1773
issn_series 1431-8598
copyrightSpringer-Verlag New York 2009
The information of publication is updating

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发表于 2025-3-21 22:11:37 | 显示全部楼层
Allan GutSecond edition features a new chapter on perturbed random walks, which are modeled as random walks plus “noise”.Presents updates to the first edition, including an outlook on further results, extensio
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Springer Series in Operations Research and Financial Engineeringhttp://image.papertrans.cn/s/image/878375.jpg
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Renewal Theory for Random Walks with Positive Drift, = 0, ., where {... ≥ 1} is a sequence of i.i.d. random variables, and .. We assume throughout this chapter, unless stated otherwise, that 0 < .. = μ < ∞ (recall Theorems 2.8.2 and 2.8.3). In this section, however, no such assumption is necessary.
发表于 2025-3-23 03:45:46 | 显示全部楼层
Functional Limit Theorems,eans that one considers the partial sums {.., ..,..., ..} of i.i.d. variables jointly for each n and shows that if the mean and variance are finite then the (polygonal) process obtained by normalization (and linear interpolation), behaves, asymptotically, like Brownian motion.
发表于 2025-3-23 07:49:11 | 显示全部楼层
Perturbed Random Walks,s covered in Chapter 3 and onwards. The next one was considered in Section 4.5, namely “time dependent” boundaries. Since the appearance of the first edition of this book in 1988 research in the area has moved on. In this chapter we present some of the post-1988 development.
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