ENGLISH

Random probability measures on Polish spaces

By Hans Crauel

Book information

Publisher
CRC Press
Year
2002
ISBN
9780415273879, 0415273870
Open Library ID
OL18138933M
Language
english
Format
PDF
Filesize
4 MB (4212589 bytes)
Series
Stochastics Monographs
Edition
1
Pages
137\137
Time added
2009-08-06 05:14:26

Description

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.

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