Infinitesimal generators for a class of polynomial processes
Volume 229 / 2015
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.