Markov Processes Involving q-Stirling Numbers

In this paper we consider the Markov process de ned by P Pn n Pn n Pn for transition probabilities n q and n q We give closed forms for the distributions and the moments of the underlying random variables Thereby we observe that the distributions can be easily described in terms of q Stirling numbers of the second kind Their occurrence in a purely time dependent Markov process allows a natural approximation for these numbers through the normal distribution We also show that these Markov processes describe some parameters related to the study of random graphs as well as to the analysis of algorithms