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Hypergroups and Quantum Bessel Processes of Non-integer Dimensions

Author

Listed:
  • Wojciech Matysiak

    (Politechnika Warszawska)

Abstract

It is demonstrated how to use a certain family of commutative hypergroups to provide a universal construction of Biane’s quantum Bessel processes of all dimensions not smaller than 1. The classical Bessel processes $$\text {BES}(\delta )$$ BES ( δ ) are analogously constructed with the aid of the Bessel–Kingman hypergroups for all, not necessarily integer, dimensions $$\delta \ge 1$$ δ ≥ 1 .

Suggested Citation

  • Wojciech Matysiak, 2017. "Hypergroups and Quantum Bessel Processes of Non-integer Dimensions," Journal of Theoretical Probability, Springer, vol. 30(4), pages 1677-1691, December.
    • Handle: RePEc:spr:jotpro:v:30:y:2017:i:4:d:10.1007_s10959-016-0688-2
    DOI: 10.1007/s10959-016-0688-2
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    References listed on IDEAS

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    1. Michael Voit, 2009. "Bessel Convolutions on Matrix Cones: Algebraic Properties and Random Walks," Journal of Theoretical Probability, Springer, vol. 22(3), pages 741-771, September.
    2. Matysiak, Wojciech & Świeca, Marcin, 2015. "Zonal polynomials and a multidimensional quantum Bessel process," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3430-3457.
    3. Bryc, Wlodzimierz & Wesolowski, Jacek, 2006. "The classical bi-Poisson process: An invertible quadratic harness," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1664-1674, September.
    Full references (including those not matched with items on IDEAS)

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