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Duality and Multiplicative Stochastic Processes on Quantum Groups

Author

Listed:
  • Philip Feinsilver

    (Southern Illinois University)

  • Uwe Franz

    (TU Clausthal
    Université Nancy I)

  • René Schott

    (Université Nancy I)

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.

Suggested Citation

  • Philip Feinsilver & Uwe Franz & René Schott, 1997. "Duality and Multiplicative Stochastic Processes on Quantum Groups," Journal of Theoretical Probability, Springer, vol. 10(3), pages 795-818, July.
    • Handle: RePEc:spr:jotpro:v:10:y:1997:i:3:d:10.1023_a:1022618114810
    DOI: 10.1023/A:1022618114810
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