Nous donnons une relation entre le signe de l’espérance d’une variable aléatoire à valeurs entières minorées et le nombre des zéros de dans le disque unité où est la fonction génératrice de et ce sous des conditions peu exigeantes.
We give a relation between the sign of the mean of an integer-valued, left bounded, random variable and the number of zeros of inside the unit disk, where is the generating function of , under some mild conditions
@article{BSMF_2008__136_4_565_0,
author = {Delorme, Charles and Rinkel, Jean-Marc},
title = {About the generating function of a left bounded integer-valued random variable},
journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
volume = {136},
year = {2008},
pages = {565-573},
doi = {10.24033/bsmf.2566},
mrnumber = {2443036},
zbl = {1158.60013},
language = {en},
url = {http://dml.mathdoc.fr/item/BSMF_2008__136_4_565_0}
}
Delorme, Charles; Rinkel, Jean-Marc. About the generating function of a left bounded integer-valued random variable. Bulletin de la Société Mathématique de France, Tome 136 (2008) pp. 565-573. doi : 10.24033/bsmf.2566. http://gdmltest.u-ga.fr/item/BSMF_2008__136_4_565_0/
[1] - A primer on Riemann surfaces, London Mathematical Society Lecture Note Series, vol. 78, Cambridge University Press, 1984. | MR 808581 | Zbl 0546.30001
[2] & - « Application of the Toeplitz matrices to the asymptotic estimation of the potentials for random walks on the non negative integers with a left bounded generator », Prépublication de la faculté des sciences d'Orsay, 2007.
[3] - Principles of random walk, 2nd éd., Springer Verlag, 2001. | MR 388547 | Zbl 0359.60003