Quadratic Harnesses, q-commutations, and orthogonal martingale polynomials

Details Quadratic Harnesses, q-commutations, and orthogonal martingale polynomials Quadratic Harnesses, q-commutations, and orthogonal martingale polynomials

2005-04-10

arxiv.org/abs/math/0504194v1

Trans. Amer. Math. Soc. 359 (2007), no. 11, 5449--5483.

Mathematics

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Scientific paper

We 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.

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