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
Abstract
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.
