Limiting characteristics for finite birth-death-catastrophe processes

Alexander Zeifman; Yakov Satin; Tatyana Panfilova

doi:10.1016/j.mbs.2013.02.009

Limiting characteristics for finite birth-death-catastrophe processes

Math Biosci. 2013 Sep;245(1):96-102. doi: 10.1016/j.mbs.2013.02.009. Epub 2013 Mar 1.

Authors

Alexander Zeifman¹, Yakov Satin, Tatyana Panfilova

Affiliation

¹ Vologda State Pedagogical University, Institute of Informatics Problems RAS, and ISEDT RAS, S. Orlova 6, Vologda, Russia. a_zeifman@mail.ru

PMID: 23458510
DOI: 10.1016/j.mbs.2013.02.009

Abstract

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.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Animals
Biostatistics
Humans
Markov Chains
Mathematical Concepts
Models, Biological
Population Dynamics / statistics & numerical data*
Stochastic Processes