World Scientific Publishing Company Structural Aspects In The Theory Of Probability (2Nd Enlarged Edition): 8 (Series On Multivariate Analysis)

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 SturmLiouville hypergroups, and on the central limit problem for groups such as tori, p-adic groups and solenoids. Review This is an attractive book. --Short Book ReviewsThis book is well organized and very readable. The list of frequently used symbols and the index are useful. It is made as self-contained and simple as is possible and reasonable. --Mathematical ReviewsThis is a well-written, practically self-contained (and suitable for courses) account of the Lévy-Khinchin representation of infinitely divisible measures and convolution semigroups in two settings. --Zentralblatt MATH From the Back Cover 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 SturmLiouville hypergroups, and on the central limit problem for groups such as tori, p-adic groups and solenoids.