The main topic of this paper is the composition of independent Poisson processes of which we study the probability law (involving Bell polynomials), the governing equations, and its representation as a random sum. Some compositions of Poisson processes with the inverses of classical and fractional Poisson processes, and with the inverse of the fractional linear birth process, are examined and their pricipal features analysed.
Composition of Poisson Processes
POLITO, Federico
2010-01-01
Abstract
The main topic of this paper is the composition of independent Poisson processes of which we study the probability law (involving Bell polynomials), the governing equations, and its representation as a random sum. Some compositions of Poisson processes with the inverses of classical and fractional Poisson processes, and with the inverse of the fractional linear birth process, are examined and their pricipal features analysed.
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