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arXiv · 1109.0180

Transient analysis of the subordinated chain of a state dependent pure birth process

Andrea Monsellato
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Abstract

Consider a pure birth process with intensities {\lambda}(k) =1/(1+k), with k=0,1,2,..., we show that the subordinated chain is assimilable to a Bernoullian scheme with dependent successes probabilities, also we show a direct link with a degenerate Polya urn replacement scheme \cite{Janson}. We compute explicitly transition probabilities, by generating function method, of the subordinated chain and give some interesting bounds using the "centering sequence" approach proposed by MacDiarmid \cite{McDiarmidcentering}.

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Andrea Monsellato. 2011-09-01. Transient analysis of the subordinated chain of a state dependent pure birth process. https://arxiv.org/abs/1109.0180

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