Quadratic harnesses, $q$-commutations, and orthogonal martingale polynomials

• Autores: Wlodzimierz Bryc, Wojciech Matysiak, Jacek Weskowski
• Localización: Transactions of the American Mathematical Society, ISSN 0002-9947, Vol. 359, Nº 11, 2007, págs. 5449-5483
• Idioma: inglés
• DOI: 10.1090/s0002-9947-07-04194-3
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• Resumen

  • 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.