The monotone Poisson process

Tom 73 / 2006

Alexander C. R. Belton Banach Center Publications 73 (2006), 99-115 MSC: Primary 46L53; Secondary 11B73, 60G44, 81S25. DOI: 10.4064/bc73-0-6


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.


  • Alexander C. R. BeltonInstitut Girard Desargues
    Université Claude Bernard Lyon 1
    43 avenue du 11 novembre 1918
    Villeurbanne 69622 Cedex, France

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