The coefficients of the moments of the monotone Poisson law are shown to be a type of Stirling number of the first kind; certain combinatorial identities relating to these numbers are proved and a new derivation of the Cauchy transform of this law is given. An investigation is begun into the classical Azéma-type martingale which corresponds to the compensated monotone Poisson process; it is shown to have the chaotic-representation property and its sample paths are described.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-6,
author = {Alexander C. R. Belton},
title = {The monotone Poisson process},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {99-115},
zbl = {1109.46052},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-6}
}
Alexander C. R. Belton. The monotone Poisson process. Banach Center Publications, Tome 72 (2006) pp. 99-115. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-6/