Structural aspects in the theory of probability
著者
書誌事項
Structural aspects in the theory of probability
（Series on multivariate analysis, v. 8）
World Scientific, c2010
2nd enl. ed. / with an additional chapter by Gyula Pap
- : hard
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注記
Includes bibliographical references (p. 389-395) and index
内容説明・目次
内容説明
The book is conceived as a text accompanying the traditional graduate courses on probability theory. An important feature of this enlarged version is the emphasis on algebraic-topological aspects 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. Fourier transformation - the method applied within the settings of Banach spaces, locally compact Abelian groups and commutative hypergroups - is given an in-depth discussion. This powerful analytic tool along with the relevant facts of harmonic analysis make it possible to study certain properties of stochastic processes in dependence of the algebraic-topological structure of their state spaces. In extension of the first edition, the new edition contains chapters on the probability theory of generalized convolution structures such as polynomial and Sturm-Liouville hypergroups, and on the central limit problem for groups such as tori, p-adic groups and solenoids.
目次
- Probability Measures on Metric Spaces
- The Fourier Transform in a Banach Space
- The Structure of Infinitely Divisible Probability Measures
- Harmonic Analysis of Convolution Semigroups
- Negative Definite Functions and Convolution Semigroups
- Probabilistic Properties of Convolution Semigroups
- Hypergroups in Probability Theory
- Limit Theorems on Locally Compact Abelian Groups.
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