On the Approach to Obtaining Perturbation Bounds for a Class of Birth-Death Processes

An approach is considered for obtaining perturbation bounds for inhomogeneous birth and death processes. We also considered the situation when the monotonicity conditions are satisfied for two homogeneous Markov chains
$X$
and
$X$
, and for a non-homogeneous Markov chain
$\tilde{X}(t)$
. Under these conditions, some limiting characteristics
$\tilde{X}(t)$
were studied. This approach is reduced to the study of the forward Kolmogorov system of the corresponding processes, and it can be generalized for a more general class of Markov chains with continuous time for the study of limiting characteristics. A numerical example is also considered, in which the forward Kolmogorov system was solved by the Runge-Kutta method of the 4th order.