Probability Measures on Metric Spaces

K.R. Parthasarathy

ISBN 10: 1470481103 / ISBN 13: 9781470481100

Edité par American Mathematical Society, US, 1967

A propos de cet article

In this book, the author gives a cohesive account of the theory of probability measures on complete metric spaces (which is viewed as an alternative approach to the general theory of stochastic processes). After a general description of the basics of topology on the set of measures, the author discusses regularity, tightness, and perfectness of measures, properties of sampling distributions, and metrizability and compactness theorems. Next, he describes arithmetic properties of probability measures on metric groups and locally compact abelian groups. Covered in detail are notions such as decomposability, infinite divisibility, idempotence, and their relevance to limit theorems for ""sums"" of infinitesimal random variables. The book concludes with numerous results related to limit theorems for probability measures on Hilbert spaces and on the space of continuous functions on an interval. This book is suitable for graduate students and researchers interested in probability and stochastic processes and would make an ideal supplementary reading or independent study text.

N° de réf. du vendeur LU-9781470481100

Détails bibliographiques

• Titre: Probability Measures on Metric Spaces
• Éditeur: American Mathematical Society, US
• Date de parution: 1967
• Langue: anglais
• ISBN à 10 chiffres: 1470481103
• ISBN à 13 chiffres: 9781470481100
• Reliure: Paperback
• État de l'article: New

A propos de ce titre

Synopsis

In this book, the author gives a cohesive account of the theory of probability measures on complete metric spaces (which is viewed as an alternative approach to the general theory of stochastic processes). After a general description of the basics of topology on the set of measures, the author discusses regularity, tightness, and perfectness of measures, properties of sampling distributions, and metrizability and compactness theorems. Next, he describes arithmetic properties of probability measures on metric groups and locally compact abelian groups. Covered in detail are notions such as decomposability, infinite divisibility, idempotence, and their relevance to limit theorems for "sums" of infinitesimal random variables. The book concludes with numerous results related to limit theorems for probability measures on Hilbert spaces and on the space of continuous functions on an interval. This book is suitable for graduate students and researchers interested in probability and stochastic processes and would make an ideal supplementary reading or independent study text.