English

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

Probability 2013-02-25 v2

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}.

Keywords

Cite

@article{arxiv.1109.0180,
  title  = {Transient analysis of the subordinated chain of a state dependent pure birth process},
  author = {Andrea Monsellato},
  journal= {arXiv preprint arXiv:1109.0180},
  year   = {2013}
}