Structural Aspects In The Theory Of Probability (2nd Enlarged Edition)
Author | : Herbert Heyer |
Publisher | : World Scientific |
Total Pages | : 425 |
Release | : 2009-09-03 |
ISBN-10 | : 9789814466943 |
ISBN-13 | : 9814466948 |
Rating | : 4/5 (43 Downloads) |
Book excerpt: 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.