by Herbert Heyer (Universität Tübingen, Germany)

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.

This book has been selected for coverage in:

• CC / Physical, Chemical & Earth Sciences

• Index to Scientific Book Contents® (ISBC)

• 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