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Stochastic Processes and Operator Calculus on Quantum Groups (Hardcover, 1999 ed.)
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Stochastic Processes and Operator Calculus on Quantum Groups (Hardcover, 1999 ed.)
Series: Mathematics and Its Applications, 490
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Quantum groups have been investigated rather deeply in mathematical
physics over the last decade. Among the most prominent
contributions in this area let us mention the works of V.G.
Drinfeld, S.L. Woronowicz, S. Majid. Prob ability the- ory on
quantum groups has developed in several directions (see works of P.
Biane, RL. Hudson and K.R Partasarathy, P.A. Meyer, M. Schurmann,
D. Voiculescu). The aim of this book is to 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 ma- terial is scattered throughout available
literature, however, we have nowhere found in accessible form all
of this material collected. The presentation of representation
theory in connection with Appell systems is original with the
authors. Stochastic processes (example: Brownian motion, diffusion
processes, Levy processes) are in- vestigated and several examples
are presented. As a text the work is intended to be accessible to
graduate students and researchers not specialised in quantum prob
ability. We would like to acknowledge our colleagues P. Feinsilver,
R Lenzceswki, D.
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