by Herbert Heyer (Universität Tübingen, Germany)

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.

• 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