The monotone Poisson process
Volume 73 / 2006
Banach Center Publications 73 (2006), 99-115
MSC: Primary 46L53; Secondary 11B73, 60G44, 81S25.
DOI: 10.4064/bc73-0-6
Abstract
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.
