This book focuses on the algebraic-topological aspects of probability theory, leading to a wider and deeper understanding of basic theorems, such as those on the structure of continuous convolution semigroups and the corresponding processes with independent increments. The method applied within the setting of Banach spaces and of locally compact Abelian groups is that of the Fourier transform. This analytic tool along with the relevant parts of harmonic analysis makes it possible to study certain properties of stochastic processes in dependence of the algebraic-topological structure of their state spaces. Graduate students, lecturers and researchers may use the book as a primer in the theory of probability measures on groups and related structures.
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...well-written, practically self-contained. -- Zentralblatt MATH
Well organized and very readable. -- Mathematical Reviews
Well organized and very readable. -- Mathematical Reviews
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Inside This Book
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First Sentence:
Let (E, d) denote a metric space, O(E), A(E), K(E) the systems of open, closed and compact subsets of E respectively. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
centralizing sequence, continuous negative definite function, convolution semigroups, divisible probability measures, positive definite measures, negative definite functions, filtered family, continuity theorem, invariance group, open subgroup, positive hermitian, symmetric measure, compact sequence, dual pair, closed subgroup, locally compact group, second countable, positive definite functions, topological vector spaces Key Phrases - Capitalized Phrases (CAPs): (learn more)
Applying Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Let (E, d) denote a metric space, O(E), A(E), K(E) the systems of open, closed and compact subsets of E respectively. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
centralizing sequence, continuous negative definite function, convolution semigroups, divisible probability measures, positive definite measures, negative definite functions, filtered family, continuity theorem, invariance group, open subgroup, positive hermitian, symmetric measure, compact sequence, dual pair, closed subgroup, locally compact group, second countable, positive definite functions, topological vector spaces Key Phrases - Capitalized Phrases (CAPs): (learn more)
Applying Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 10
books:
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- Probability and Mathematical Statistics by Eugene Lukacs in Back Matter
- Mathematical Methods in Sample Surveys (Series on Multivariate Analysis, Vol 3) by Howard G. Tucker in Front Matter
- Multidimensional Second Order Stochastic Processes (Series on Multivariate Analysis, Vol. 2) by Yuichiro Kakihara in Front Matter
- Abstract Methods in Information Theory (Series on Multivariate Analysis, Volume 4) by Yuichiro Kakihara in Front Matter
- Functional Analysis (Springer Classics in Mathematics) by Kosaku Yosida in Back Matter
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