Theory of Probability and Mathematical Statistics
Point processes subordinated to compound Poisson processes
K. V. Kobylych, L. M. Sakhno
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Abstract: We investigate point processes $N^f (t)=N(H^f(t))$, $t>0$, where $N(t)$ is a Poisson process and $H^f(t)$ is the subordinator with Bern\u{s}tein function $f(\lambda)$. For the case when $H^f(t)$ is the compound Poisson process with gamma distributed jumps we present probabilistic distribution and moments of the first and second order of the processes $N^f(t)$, and also consider these processes with double and iterated time change.
Keywords: Point processes, Poisson processes, compound Poisson processes, Bernstein function,subordinators
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