This book aims to present several new developments on stochastic processes and operator calculus on quantum groups. Topics which are treated include operator calculus, dual representations, stochastic processes and diffusions, Appell polynomials and systems in connection with evolution equations. Audience: This volume contains introductory material for graduate students who are new to the field, as well as more advanced material for specialists in probability theory, algebraic structures, representation theory, mathematical physics and theoretical physics.
Franz (Ernst-Moritz-Arndt-Universit<:a>t Greigwald, Germany) and Schott (Universit<'e> Henri Poincar<'e>-Nancy, France) present several new aspects related to quantum groups<-->operator calculus, dual representations, stochastic processes and diffusions, Appell polynomials and systems in connection with evolution equations. Much of the material can be found scattered throughout available literature, however, the presentation of representation theory in connection with Appell systems is original. Stochastic processes, such as Brownian motion, diffusion processes and L<'e>vy processes, are investigated, and several examples are presented. The text is accessible to graduate students and researchers not specialized in quantum probability. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Preface. 1. Introduction. 2. Preliminaries on Lie groups. 3. Hopf algebras, quantum groups and braided spaces. 4. Stochastic Processes on quantum groups. 5. Markov Structure of quantum Lévy Processes. 6. Diffusions on braided spaces. 7. Evolution equations and Lévy processes on quantum groups. 8. Gauss Laws in the sense of Bernstein on quantum groups. 9. Phase retrieval for probability distributions on quantum groups. 10. Limit theorems on quantum groups. Bibliography. Index.