General nonstationary birth-death process with possible catastrophes on finite state space is studied. The approach for obtaining the bounds on the rates of convergence to the limiting characteristics is outlined. Method for construction of the limiting characteristics is proposed. We also show that, as a rule, the initial conditions quickly become irrelevant. An example of respective process is shown in details.
Keywords: Limiting characteristics; Nonstationary birth–death process; TKF91 model; Weak ergodicity.
Copyright © 2013 Elsevier Inc. All rights reserved.