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

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