About the generating function of a left bounded integer-valued random variable
Charles Delorme; Jean-Marc Rinkel
Bulletin de la Société Mathématique de France (2008)
- Volume: 136, Issue: 4, page 565-573
- ISSN: 0037-9484
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topDelorme, Charles, and Rinkel, Jean-Marc. "About the generating function of a left bounded integer-valued random variable." Bulletin de la Société Mathématique de France 136.4 (2008): 565-573. <http://eudml.org/doc/272414>.
@article{Delorme2008,
abstract = {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 $1-\Phi (z)$ inside the unit disk, where $\Phi $ is the generating function of $X$, under some mild conditions},
author = {Delorme, Charles, Rinkel, Jean-Marc},
journal = {Bulletin de la Société Mathématique de France},
keywords = {random walk; random variable; generating function},
language = {eng},
number = {4},
pages = {565-573},
publisher = {Société mathématique de France},
title = {About the generating function of a left bounded integer-valued random variable},
url = {http://eudml.org/doc/272414},
volume = {136},
year = {2008},
}
TY - JOUR
AU - Delorme, Charles
AU - Rinkel, Jean-Marc
TI - About the generating function of a left bounded integer-valued random variable
JO - Bulletin de la Société Mathématique de France
PY - 2008
PB - Société mathématique de France
VL - 136
IS - 4
SP - 565
EP - 573
AB - 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 $1-\Phi (z)$ inside the unit disk, where $\Phi $ is the generating function of $X$, under some mild conditions
LA - eng
KW - random walk; random variable; generating function
UR - http://eudml.org/doc/272414
ER -
References
top- [1] A. F. Beardon – A primer on Riemann surfaces, London Mathematical Society Lecture Note Series, vol. 78, Cambridge University Press, 1984. Zbl0546.30001MR808581
- [2] C. Delorme & J.-M. Rinkel – « 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] F. Spitzer – Principles of random walk, 2nd éd., Springer Verlag, 2001. Zbl0359.60003MR388547
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