Titlebook: Stochastic Processes and Operator Calculus on Quantum Groups; Uwe Franz,René Schott Book 1999 Springer Science+Business Media Dordrecht 19

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,Evolution equations and Lévy processes on quantum groups,ons can be given as Appell systems or shifted moments of the associated process, and show how these can be calculated explicitly on the q-affine group and on a braided analogue of the Heisenberg-Weyl group.

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https://doi.org/10.1007/978-94-015-9277-2Algebraic structure; Lévy process; Probability theory; Theoretical physics; calculus; mathematical physic

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Stochastic processes on quantum groups,In this chapter we define Lévy processes on involutive bialgebras. These processes appeared first in the work of von Waldenfels[Wal73], the algebraic framework for the general theory of these processes was formulated in [ASW88]. For the development of the theory until 1993 see also [Sch93].

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,Markov structure of quantum Lévy processes,here exists a classical stochastic process (X͂.). on some probability space (Ω, ., .) such that all time-ordered moments agree, i.e. .for all ., ..,..., .. ∈ IN, .. ≤ ... ≤ .. ≤ ., for the (vacuum) state Φ.