Duality and Multiplicative Stochastic Processes on Quantum Groups

Philip Feinsilver, Uwe Franz and René Schott
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Philip Feinsilver: Southern Illinois University
Uwe Franz: TU Clausthal
René Schott: Université Nancy I

Journal of Theoretical Probability, 1997, vol. 10, issue 3, 795-818

Abstract: Abstract An analogue of McKean's stochastic product integral is introduced and used to define stochastic processes with independent increments on quantum groups. The explicit form of the dual pairing (q-analogue of the exponential map) is calculated for a large class of quantum groups. The constructed processes are shown to satisfy generalized Feynman-Kac type formulas, and polynomial solutions of associated evolution equations are introduced in the form of Appell systems. Explicit calculations for Gauss and Poisson processes complete the presentation.

Keywords: Quantum groups; Appell systems; stochastic product integral (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1023/A:1022618114810

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