《停止随机 walk 的(limit theorems and applications) 真PDF》

English | PDF (True) | 2009 | 267 Pages | ISBN : 0387878343 | 3.5 MB

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”.

古典概率论提供了一定步数后的随机漫步的信息。然而，对于应用来说，考虑在随机步数后评估的随机漫步更为自然。例如，顺序分析、排队理论、存储和库存理论、保险风险理论、可靠性理论以及计数器理论。《受控随机漫步：极限定理及其应用》展示了如何使用这个理论来证明更新后的重置计数过程、首次通过时间过程以及其他某些二维随机漫步的极限定理，并且展示这些结果在各种应用中的实用性。 第二版提供了更新的内容和进一步研究成果、扩展以及推广的观点。新增一章研究非线性更新过程，以展示对受扰动的随机行走进行建模为随机行走加上“噪声”的类似理论。

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