About the generating function of a left bounded integer-valued random variable
Bulletin de la Société Mathématique de France, Volume 136 (2008) no. 4, p. 565-573

We give a relation between the sign of the mean of an integer-valued, left bounded, random variable X and the number of zeros of 1-Φ(z) inside the unit disk, where Φ is the generating function of X, under some mild conditions

Nous donnons une relation entre le signe de l’espérance d’une variable aléatoire à valeurs entières minorées et le nombre des zéros de 1-Φ(z) dans le disque unité où Φ est la fonction génératrice de X et ce sous des conditions peu exigeantes.

DOI : https://doi.org/10.24033/bsmf.2566
Classification:  60G50,  47B35,  30Cxx
Keywords: random walk, random variable, generating function
@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},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {136},
     number = {4},
     year = {2008},
     pages = {565-573},
     doi = {10.24033/bsmf.2566},
     zbl = {1158.60013},
     mrnumber = {2443036},
     language = {en},
     url = {http://www.numdam.org/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, Volume 136 (2008) no. 4, pp. 565-573. doi : 10.24033/bsmf.2566. http://www.numdam.org/item/BSMF_2008__136_4_565_0/

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