Normal martingales and polynomial families

H. Hammouch. "Normal martingales and polynomial families." Annales Polonici Mathematici 84.2 (2004): 93-102. <http://eudml.org/doc/281117>.

@article{H2004,
abstract = {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.},
author = {H. Hammouch},
journal = {Annales Polonici Mathematici},
keywords = {chaos; normal martingales; classical polynomials},
language = {eng},
number = {2},
pages = {93-102},
title = {Normal martingales and polynomial families},
url = {http://eudml.org/doc/281117},
volume = {84},
year = {2004},
}

TY - JOUR
AU - H. Hammouch
TI - Normal martingales and polynomial families
JO - Annales Polonici Mathematici
PY - 2004
VL - 84
IS - 2
SP - 93
EP - 102
AB - 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.
LA - eng
KW - chaos; normal martingales; classical polynomials
UR - http://eudml.org/doc/281117
ER -