Random Probability Measures on Polish Spaces

Stochastics Monographs

Hans Crauel

118 pages, parution le 07/08/2002

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Résumé

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.

Contents

1 Notations and Some Technical Results
2 Random Sets
3 Random Probability Measures and the Narrow Topology
4 Prohorov Theory for Random Probability Measures
5 Further Topologies on Random Measures
6 Invariant Measures and Some Ergodic theory for Random Dynamical Systems
A The Narrow Topology on Non-Random Measures
BScattered Results

L'auteur - Hans Crauel

Hans Crauel is of the Institut fur Mathematik at Technische Universitat Ilmenau in Germany.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Taylor and Francis Books
Auteur(s)	Hans Crauel
Parution	07/08/2002
Nb. de pages	118
Format	16 x 24
Couverture	Broché
Poids	335g
Intérieur	Noir et Blanc
EAN13	9780415273879
ISBN13	978-0-415-27387-9