Quadratic Harnesses, q-commutations, and orthogonal martingale polynomials

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dc.creatorBryc, Wlodzimierz
dc.creatorMatysiak, Wojciech
dc.creatorWesolowski, Jacek
dc.date2005-04-10
dc.date.accessioned2026-07-07T08:45:07Z
dc.date.available2026-07-07T08:45:07Z
dc.descriptionWe introduce the quadratic harness condition and show that integrable quadratic harnesses have orthogonal martingale polynomials with a three step recurrence that satisfies a q-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.
dc.identifierhttps://arxiv.org/abs/math/0504194
dc.identifierhttp://arxiv.org/abs/math/0504194
dc.identifierTrans. Amer. Math. Soc. 359 (2007), no. 11, 5449--5483.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142878
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60J25; 46L53
dc.titleQuadratic Harnesses, q-commutations, and orthogonal martingale polynomials
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