随机风景中的随机漫步:最近一些研究结果的调查

IF 0.6 Q4 ENGINEERING, ELECTRICAL & ELECTRONIC

International Journal of Digital Multimedia Broadcasting Pub Date : 2006-08-09 DOI:10.1214/074921706000000077

F. Hollander, J. Steif

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引用次数: 33

摘要

本文综述了近年来关于随机场景中随机漫步的一些研究成果。在$\Z^d$, $d\geq 1$上，我们得到了一个有i.d个增量的随机漫步和一个有i.d个组件的随机风景。散步和风景被认为是独立的。RWRS是一个随机过程，其中时间通过$\Z$索引，在每个时间单位中，步行所采取的步骤和所访问地点的风景价值都被记录下来。我们收集了各种结果，这些结果根据底层随机行走的特征对RWRS的遍历行为进行了分类(并讨论了对静止行走增量和静止风景组件的扩展)。我们描述了一些场景重建的结果，并通过列出一些开放的问题来结束。

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Random walk in random scenery:a survey of some recent results

In this paper we give a survey of some recent results for random walk in random scenery (RWRS). On $\Z^d$, $d\geq 1$, we are given a random walk with i.i.d. increments and a random scenery with i.i.d.\ components. The walk and the scenery are assumed to be independent. RWRS is the random process where time is indexed by $\Z$, and at each unit of time both the step taken by the walk and the scenery value at the site that is visited are registered. We collect various results that classify the ergodic behavior of RWRS in terms of the characteristics of the underlying random walk (and discuss extensions to stationary walk increments and stationary scenery components as well). We describe a number of results for scenery reconstruction and close by listing some open questions.

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来源期刊

International Journal of Digital Multimedia Broadcasting ENGINEERING, ELECTRICAL & ELECTRONIC-

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

17 weeks

期刊介绍： International Journal of Digital Multimedia Broadcasting aims to provide a high quality and timely forum for engineers, researcher and educators whose interests are in digital multimedia broadcasting to learn recent developments, to share related challenges, to compare multi-standards and further to design new and improved systems.