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Some classes of orthogonal polynomials associated with martingales. (English) Zbl 0615.60050

In T. Hida’s book ”Brownian motion.” (1980; Zbl 0432.60002) it is proved that the iterated stochastic integrals of the Brownian motion are given by corresponding Hermite polynomials. A question is raised here whether a similar phenomenon holds for other stationary independent increments processes. The answer is positive but Hermite polynomials must be replaced by Meixner polynomials.
Reviewer: L.Gal’chuk

MSC:

60H05 Stochastic integrals
60G46 Martingales and classical analysis
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)

Citations:

Zbl 0432.60002
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References:

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