q-Levy processes

Details q-Levy processes q-Levy processes

2003-09-08

arxiv.org/abs/math/0309147v2

J. Reine Angew. Math. 576 (2004), 181-207

Mathematics

Operator Algebras

A number of minor corrections; 24 pages, 1 postscript figure

Scientific paper

We continue the investigation of the Levy processes on a q-deformed full Fock space started in a previous paper. First, we show that the vacuum vector is cyclic and separating for the algebra generated by such a process. Next, we describe a chaotic representation property in terms of multiple integrals with respect to diagonal measures, in the style of Nualart and Schoutens. We define stochastic integration with respect to these processes, and calculate their combinatorial stochastic measures. Finally, we show that they generate infinite von Neumann algebras.

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