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Renewal processes decomposable into i.i.d. components
Published online by Cambridge University Press: 01 July 2016
Abstract
Let N be a stationary renewal process with a probability density function f(t). Suppose that N can be expressed as the superposition of a finite number of i.i.d. stationary components N(1), …, N(p) (p≧2). Then, under a supplementary condition on f(t), N and N(1), …, N(p) are all Poisson. This is proved by using recurrence relations given in Ito (1978) for the probability distribution of i.i.d. components of a superposition process.
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