On d-pseudo-orthogonality of the Sheffer systems associated to a convolution semigroup

• Autores: Célestin C. Kokonendji
• Localización: VIII Journées Zaragoza-Pau de Mathématiques Appliquées et de Statistiques / coord. por Manuel Pedro Palacios Latasa, David Trujillo, Juan José Torrens Iñigo, Monique Madaune-Tort, María Cruz López de Silanes Busto, Gerardo Sanz Sáiz, 2003, ISBN 84-7733-720-9, págs. 355-363
• Idioma: inglés
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• Resumen

  • We investigate which Sheffer polynomials can be associated to a convolution semigroup of probability measures, usually induced by a stochastic process with stationary and independent increments. From a recent notion of d-pseudo-orthogonality (d ? {2, 3, ? ? ?}), we characterize the associated d-pseudo-orthogonal polynomials by the class of generating probability measures, which belongs to the natural exponential family with polynomial variance functions of exact degree 2d - 1. This extends some results of (classical) orthogonality; in particular, some new sets of martingales are then pointed out. For each integer d = 2 we completely illustrate polynomials with (2d-1)-term recurrence relation for the families of positive stable processes.