3 research outputs found
On a bilateral birth-death process with alternating rates
We consider a bilateral birth-death process characterized by a constant
transition rate from even states and a possibly different transition
rate from odd states. We determine the probability generating functions
of the even and odd states, the transition probabilities, mean and variance of
the process for arbitrary initial state. Some features of the birth-death
process confined to the non-negative integers by a reflecting boundary in the
zero-state are also analyzed. In particular, making use of a Laplace transform
approach we obtain a series form of the transition probability from state 1 to
the zero-state.Comment: 13 pages, 3 figure
A review on symmetry properties of birth-death processes
In this paper we review some results on time-homogeneous birth-death
processes. Specifically, for truncated birth-death processes with two absorbing
or two reflecting endpoints, we recall the necessary and sufficient conditions
on the transition rates such that the transition probabilities satisfy a
spatial symmetry relation. The latter leads to simple expressions for
first-passage-time densities and avoiding transition probabilities. This
approach is thus thoroughly extended to the case of bilateral birth-death
processes, even in the presence of catastrophes, and to the case of a
two-dimensional birth-death process with constant rates.Comment: 16 pages, 4 figure
Random time-changes and asymptotic results for a class of continuous-time Markov chains on integers with alternating rates
We consider continuous-time Markov chains on integers which allow transitions
to adjacent states only, with alternating rates. We give explicit formulas for
probability generating functions, and also for means, variances and state
probabilities of the random variables of the process. Moreover we study
independent random time-changes with the inverse of the stable subordinator,
the stable subordinator and the tempered stable subodinator. We also present
some asymptotic results in the fashion of large deviations. These results give
some generalizations of those presented in Di Crescenzo A., Macci C.,
Martinucci B. (2014).Comment: 25 pages, 2 figure