In this paper we consider the Markov process defined by
P1,1=1,
Pn,[lscr ]=(1−λn,[lscr ])
·Pn−1,[lscr ]
+λn,[lscr ]−1
·Pn−1,[lscr ]−1
for transition probabilities
λn,[lscr ]=q[lscr ]
and
λn,[lscr ]=qn−1.
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.