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Full Description
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.
Contents
Chapters
Chapter 1. The Borel subsets of a metric space
Chapter 2. Probability measures in a metric space
Chapter 3. Probability measures in a metric group
Chapter 4. Probability measures in locally compact abelian groups
Chapter 5. The Kolmogorov consistency theorem and conditional probability
Chapter 6. Probability measures in a Hilbert space
Chapter 7. Probability measures on $C[0,1]$ and $D[0,1]$
