Transactions of the American Mathematical Society

Author(s): Wlodzimierz Bryc; Wojciech Matysiak; Jacek Wesolowski
Journal: Trans. Amer. Math. Soc. 359 (2007), 5449-5483.
MSC (2000): Primary 60J25; Secondary 46L53
Posted: June 13, 2007
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Abstract: We introduce the quadratic harness condition and show that integrable quadratic harnesses have orthogonal martingale polynomials with a three step recurrence that satisfies a

-commutation relation. This implies that quadratic harnesses are essentially determined uniquely by five numerical constants. Explicit recurrences for the orthogonal martingale polynomials are derived in several cases of interest.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 60J25, 46L53

Wlodzimierz Bryc
Affiliation: Department of Mathematics, University of Cincinnati, P.O. Box 210025, Cincinnati, Ohio 45221--0025
Email: Wlodzimierz.Bryc@UC.edu

Wojciech Matysiak
Affiliation: Faculty of Mathematics and Information Science, Warsaw University of Technology, pl. Politechniki 1, 00-661 Warszawa, Poland
Email: matysiak@mini.pw.edu.pl

Jacek Wesolowski
Affiliation: Faculty of Mathematics and Information Science, Warsaw University of Technology, pl. Politechniki 1, 00-661 Warszawa, Poland
Email: wesolo@alpha.mini.pw.edu.pl

DOI: 10.1090/S0002-9947-07-04194-3
PII: S 0002-9947(07)04194-3
Keywords: Quadratic conditional variances, harnesses, orthogonal martingale polynomials, hypergeometric orthogonal polynomials
Received by editor(s): June 8, 2005
Received by editor(s) in revised form: September 26, 2005
Posted: June 13, 2007
Additional Notes: This research was partially supported by NSF grants \#INT-0332062, \#DMS-0504198, and by the C.P. Taft Memorial Fund.
Copyright of article: Copyright 2007, American Mathematical Society

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