Infinitesimal generators for a class of polynomial processes

Jacek Wesolowski; Wlodzimierz Bryc

Infinitesimal generators for a class of polynomial processes

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arxiv 1411.6268 v2 pith:A65WZGR7 submitted 2014-11-23 math.PR math.COmath.OA

Wlodzimierz Bryc , Jacek Wesolowski This is my paper · ORCID

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keywords infinitesimalclasscommutationequationgeneratorgeneratorsharnessespolynomial

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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.

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