On a poisson hyperbolic staircase

Benny Levikson; Tomasz Rolski; Gideon Weiss

doi:10.1017/s0269964899131024

On a poisson hyperbolic staircase

Benny Levikson, Tomasz Rolski, Gideon Weiss

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a process that starts at height y, stays there for a time X₀ ∼ exp(y) when it drops to a level Z₁ ∼ U(0,y). Thereafter it stays at level Z_n for time X_n ∼ exp(Zn), then drops to a level Z_n+1 ∼ U(0,Z_n). We investigate properties of this process, as well as the Poisson hyperbolic process which is obtained by randomizing the starting point y of the above process. This process is associated with a rate 1 Poisson process in the positive quadrant: Its path is the minimal RCLL decreasing step function through Poisson points in the positive quadrant. The finite dimensional distributions are then multivariate exponential in sense of Marshall-Olkin.

Original language	English
Pages (from-to)	11-31
Number of pages	21
Journal	Probability in the Engineering and Informational Sciences
Volume	13
Issue number	1
DOIs	https://doi.org/10.1017/s0269964899131024
State	Published - 1999

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Management Science and Operations Research
Industrial and Manufacturing Engineering

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On a poisson hyperbolic staircase

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