2014•arXiv (Cornell University)Open access
Infinitesimal generators for polynomial processes
Włodek Bryc, Jacek Wesołowski
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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. We relate the infinitesimal generator to the unique solution of a certain commutation equation, and we use the commutation equation to find explicit formula for the infinitesimal generators corresponding to the so called free quadratic harnesses.