Normal martingales and polynomial families

• Autorzy: H. Hammouch
• Języki publikacji: EN

Abstrakty

EN

Wiener and compensated Poisson processes, as normal martingales, are associated to classical sequences of polynomials, namely Hermite polynomials for the first one and Charlier polynomials for the second. The problem studied in this paper is to find if there exist other normal martingales which are associated to classical sequences of polynomials. Privault, Solé and Vives [5] solved this problem via the quantum Kabanov formula under some assumptions on the normal martingales considered. We solve the problem without these assumptions and we give a complete study of this subject in Section 2. In Section 3 we introduce the notion of algebraic process and we prove that Azéma martingales are infinitely algebraic.

Kategorie tematyczne

• 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
• 60G44: Martingales with continuous parameter
• 60J55: Local time and additive functionals
• 60H05: Stochastic integrals
• 60G48: Generalizations of martingales

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2004
• Tom: 84
• Numer: 2
• Strony: 93-102

Daty

wydano

2004

Twórcy

autor

H. Hammouch

• Université d'Evry Val d'Essonne, Laboratoire d'Analyse et Probabilités, BT. Maupertuis, rue du Père Jarlan, 91025 Evry Val d'Essonne, France

Identyfikatory

DOI

10.4064/ap84-2-1