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Infinitesimal generators for a class of polynomial processes

Volume 229 / 2015

Włodzimierz Bryc, Jacek Wesołowski Studia Mathematica 229 (2015), 73-93 MSC: Primary 60J35; Secondary 47D06, 46L53. DOI: 10.4064/sm8330-12-2015 Published online: 7 December 2015


We study the infinitesimal generators of evolutions of linear mappings on the space of polynomials, which correspond to a special class of Markov processes with polynomial regressions called quadratic harnesses. We relate the infinitesimal generator to the unique solution of a certain commutation equation, and we use the commutation equation to find an explicit formula for the infinitesimal generator of free quadratic harnesses.


  • Włodzimierz BrycDepartment of Mathematics
    University of Cincinnati
    PO Box 210025
    Cincinnati, OH 45221--0025, U.S.A.
  • Jacek WesołowskiFaculty of Mathematics and Information Science
    Warsaw University of Technology
    pl. Politechniki 1
    00-661 Warszawa, Poland

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