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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm8330-12-2015,
author = {W\l odzimierz Bryc and Jacek Weso\l owski},
title = {Infinitesimal generators for a class of polynomial processes},
journal = {Studia Mathematica},
volume = {231},
year = {2015},
pages = {73-93},
zbl = {06526962},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8330-12-2015}
}
Włodzimierz Bryc; Jacek Wesołowski. Infinitesimal generators for a class of polynomial processes. Studia Mathematica, Tome 231 (2015) pp. 73-93. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8330-12-2015/