Probability Measures on Metric Spaces

K.r. Parthasarathy

ISBN 10: 082183889X / ISBN 13: 9780821838891

Published by American Mathematical Society, 2005

Presents an account of the theory of probability measures on complete metric spaces. This title includes a description of the basics of topology on the set of measures. It discusses regularity, tightness, and perfectness of measures, properties of sampling . Seller Inventory # 613929324

Synopsis:

Having been out of print for over 10 years, the AMS is delighted to bring this classic volume back to the mathematical community. With this fine exposition, the author gives a cohesive account of the theory of probability measures on complete metric spaces (which he views 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, he 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 spaces $C[0,1]$. ""The Mathematical Reviews"" comments about the original edition of this book are as true today as they were in 1967. It remains a compelling work and a priceless resource for learning about the theory of probability measures. The volume is suitable for graduate students and researchers interested in probability and stochastic processes and would make an ideal supplementary reading or independent study text.

Bibliographic Details

Title: Probability Measures on Metric Spaces
Publisher: American Mathematical Society
Publication Date: 2005
Binding: Einband - fest (Hardcover)
Condition: New