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Markov processes with free-Meixner laws

Author

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  • Bryc, Wlodek

Abstract

We study a time-non-homogeneous Markov process which arose from free probability, and which also appeared in the study of stochastic processes with linear regressions and quadratic conditional variances. Our main result is the explicit expression for the generator of the (non-homogeneous) transition operator acting on functions that extend analytically to complex domains. The paper is self-contained and does not use free probability techniques.

Suggested Citation

  • Bryc, Wlodek, 2010. "Markov processes with free-Meixner laws," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1393-1403, August.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:8:p:1393-1403
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    Cited by:

    1. Bryc, Włodek & Fakhfakh, Raouf & Hassairi, Abdelhamid, 2014. "On Cauchy–Stieltjes kernel families," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 295-312.
    2. Bryc, Wlodzimierz & Wesołowski, Jacek, 2014. "Infinitesimal generators of q-Meixner processes," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 915-926.
    3. Hiroaki Yoshida, 2020. "Remarks on a Free Analogue of the Beta Prime Distribution," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1363-1400, September.

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