This book aims to present several new developments on shastic processes and operator calculus on quantum groups. Topics which are treated include operator calculus, dual representations, shastic 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.
Table of ContentsPreface. 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.