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08 February 2025
 
  » arxiv » 1109.0180

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Transient analysis of the subordinated chain of a state dependent pure birth process
Andrea Monsellato ;
Date 1 Sep 2011
AbstractConsider a pure birth process with intensities $lambda_{k}=frac{1}{1+k}$, 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 emph{centering sequence} approach proposed by MacDiarmid cite{McDiarmidcentering}.
Source arXiv, 1109.0180
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