White noise on bialgebras
By: Michael Schürmann.
Series: Lecture notes in mathematics ;; 1544; Lecture notes in mathematics (Springer-Verlag) ;; 1544.
Publisher: Springer-Verlag
Published: 1993
Place of publication: Berlin; New York
Language: eng
Number of pages: 146
Subjects: Quantum theory -- Mathematics.; Stochastic analysis.
Description: Stochastic processes with independent increments on a group are generalized to the concept of "white noise" on a Hopf algebra or bialgebra. The main purpose of the book is the characterization of these processes as solutions of quantum stochastic differential equations in the sense of R.L. Hudsonand K.R. Parthasarathy. The notes are a contribution to quantum probability but they are also related to classical probability, quantum groups, and operator algebras. The Az ma martingales appear as examples of white noise on a Hopf algebra which is a deformation of the Heisenberg group. The book will be of interest to probabilists and quantum probabilists. Specialists in algebraic structures who are curious about the role of their concepts in probablility theory as well as quantum theory may find the book interesting. The reader should havesome knowledge of functional analysis, operator algebras, and probability theory.
Notes: Includes bibliographical references (p. [138]-142) and index.