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arXiv · 1411.6268

Infinitesimal generators for a class of polynomial processes

Wlodzimierz Bryc·Jacek Wesolowski
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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 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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Wlodzimierz Bryc, Jacek Wesolowski. 2015-11-19. Infinitesimal generators for a class of polynomial processes. https://doi.org/10.4064/sm8330-12-2015

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