Poisson thinning by monotone factors.

Ball, Karen

Displaying similar documents to “Poisson thinning by monotone factors.”

The monotone Poisson process

Alexander C. R. Belton (2006)

Banach Center Publications

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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. ...

Corners and records of the Poisson process in quadrant.

Gnedin, Alexander (2008)

Electronic Communications in Probability [electronic only]

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Remarks on the Poisson stochastic process (III) (On a property of the homogeneous Poisson process)

C. Ryll-Nardzewski (1954)

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A dynamical characterization of Poisson-Dirichlet distributions.

Arguin, Louis-Pierre (2007)

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Statistical problems on point processes

Klaus Krickeberg (1980)

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Z. Schenková (1982)

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Convergence in distribution for subset counts between random sets.

Stark, Dudley (2004)

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The cluster size distribution for a forest-fire process on $ℤ$ .

Brouwer, Rachel M., Pennanen, Juho (2006)

Electronic Journal of Probability [electronic only]

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The structure distribution in a mixed Poisson process.

Teugels, Jozef L., Vynckier, Petra (1996)

Journal of Applied Mathematics and Stochastic Analysis

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The monotone cumulants

Takahiro Hasebe, Hayato Saigo (2011)

Annales de l'I.H.P. Probabilités et statistiques

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In the present paper we define the notion of generalized cumulants which gives a universal framework for commutative, free, Boolean and especially, monotone probability theories. The uniqueness of generalized cumulants holds for each independence, and hence, generalized cumulants are equal to the usual cumulants in the commutative, free and Boolean cases. The way we define (generalized) cumulants needs neither partition lattices nor generating functions and then will give a new viewpoint...