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Free quadratic harness

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Mar 2011Embargo end date: 01 Jan 2010 English Publisher:Elsevier BVJournal:Stochastic Processes and their Applications, volume 121, pages 657-671 (issn: 0304-4149,

Authors: Jacek Wesołowski; Wojciech Matysiak; Wlodzimierz Bryc;

doi: 10.1016/j.spa.2010.11.013 , 10.48550/arxiv.1003.4771

arXiv: http://arxiv.org/abs/1003.4771

Free quadratic harness

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Abstract

Free quadratic harness is a Markov process from the class of quadratic harnesses, i.e. processes with linear regressions and quadratic conditional variances. The process has recently been constructed for a restricted range of parameters in the paper "Askey-Wilson polynomials, quadratic harnesses and martingales" by W. Bryc and J. Weso��owski using Askey--Wilson polynomials. Here we provide a self-contained construction of the free quadratic harness for all values of parameters.

Related Organizations

University System of Ohio
United States
University of Cincinnati
United States
Warsaw University of Technology
Poland
University of Cincinnati Main Campus
United States

Keywords

Probability (math.PR), FOS: Mathematics, Mathematics - Probability

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NSF| Research on classical and non-commutative probability