Probability Measures on Metric Spaces
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.
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Chapter IThe Borel Subsets of a Metric Space
Chapter IIProbability Measures in a Metric Space
Chapter IIIProbability Measures in a Metric Group
The Case When X Is Abelian
Chapter IVProbability Measures in Locally Compact Abelian Groups 1 Introduction
Preliminary Facts about a Group and Its Character Group
Infinitely Divisible Distributions
The Consistency Theorem in the Case of Inverse Limits of Borel Spaces
The Extension Theorem
The Kolmogorov Consistency Theorem
Statement of the Second Problem
Existence of Conditional Probability
Regular Conditional Probability
Chapter VIProbability Measures in a Hilbert Space 1 Introduction
An Estimate of the Variance
General Limit Theorems for Sums of Infinitesimal Summands
Representation of Infinitely Divisible Distributions
Uniqueness of the Representation
Representation of Convolution Semigroups
A Decomposition Theorem
Absolutely Continuous Indecomposable Distributions in X
Chapter VThe Kolmogorov Consistency Theorem and Conditional Probability 1 Statement of the First Problem
Standard Borel Spaces
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JSTOR: Probability Measures on Metric Spaces.
Probability Measures on Metric Spaces. kr Parthasarathy, Academic Press, New York, 1967, pp. 276, $12.00. bls PRAKASA RAO, University of Illinois A LARGE ...
PROBABILITY MEASURES ON METRIC SPACES By kr pp. xi, 276; 112 ...
PROBABILITY MEASURES ON METRIC SPACES. By kr. PARTHASARATHY:. pp. xi, 276; 112$. (Academic Press Inc., New York,. 1967). Professor Parthasarathy's new book ...
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Review: kr Parthasarathy, Probability Measures on Metric Spaces
kr Parthasarathy, Probability Measures on Metric Spaces. Full-text: Access by subscription. PDF File (92 KB). Links and Identifiers ...
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OPEN MAPPING THEOREMS FOR PROBABILITY MEASURES ON METRIC SPACES 1 ...
PROBABILITY MEASURES ON METRIC SPACES. LARRY Q. EIFLER. Let 5 and T denote complete separable metric spaces. Let. P(S) denote the collection of probability ...
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Kannan, Kannappan: On a characterization of gaussian measures in a ...
 kr PARTHASARATHY, Probability Measures on Metric Spaces. Academic Press, New York, 1967.  Yu. V. PROKHOROV and M. FISH, A characterization of normal ...
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Phys. Rev. Lett. 62, 1339 (1989): Carfora and Marzuoli ...
kr Parthasarathy, Probability Measures on Metric Spaces (Academic, New York, 1967). Notice that we may be tempted to characterize the measure P through the ...
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Probability measures on metric spaces
Probability measures on metric spaces. Onno van Gaans. These are some loose notes supporting the first sessions of the seminar Stochastic ...
www.math.leidenuniv.nl/ ~vangaans/ jancol1.pdf
New Publications Offered by the AMS, Volume 52, Number 8
958. N. OTICES OF THE. AMS. V. OLUME. 52, N. UMBER. 8. New Publications. Offered by the AMS. Analysis. Complex Analysis. and Dynamical. Systems II ...
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Probability measures on metric spaces. - / 1967 - Livros
Título Principal, Probability measures on metric spaces [by] kr Parthasarathy. Publicação, New York : Academic Press, 1967. Descrição Física, xi, 276 p. ...
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Getoor, Sharpe: The Ray space of a right process
 kp PARTHASARATHY, Probability Measures on Metric Spaces, Aca demic Press, New York (1967).  db RAY, Resolvents, transition functions, and strongly ...
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