Random Probability Measures on Polish Spaces 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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Crauel, Hans 作者

CRC Pr I Llc

译者

2002-7 出版日期

136 页数

$ 124.24 价格

HRD

丛书系列

9780415273879 图书编码

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Random Probability Measures on Polish Spaces 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

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In this monograph the narrow topology on random probability measures on Polish spaces is investigated in a thorough and comprehensive way. As a special feature, no additional assumptions on the probability space in the background, such as completeness or a countable generated algebra, are made. One of the main results is a direct proof of the random analog of the Prohorov theorem, which is obtained without invoking an embedding of the Polish space into a compact space. Further, the narrow topology is examined and other natural topologies on random measures are compared. In addition, it is shown that the topology of convergence in law-which relates to the "statistical equilibrium"-and the narrow topology are incompatible. A brief section on random sets on Polish spaces provides the fundamentals of this theory. In a final section, the results are applied to random dynamical systems to obtain existence results for invariant measures on compact random sets, as well as uniformity results in the individual ergodic theorem. This clear and incisive volume is useful for graduate students and researchers in mathematical analysis and its applications.

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