Complutense University Library

Quasi-stationary and ratio of expectations distributions: A comparative study

Artalejo, Jesús R. and López-Herrero, M.J. (2010) Quasi-stationary and ratio of expectations distributions: A comparative study. Journal of Theoretical Biology, 266 (2). pp. 264-274. ISSN 0022-5193

[img] PDF
Restricted to Repository staff only until 31 December 2020.

367kB

Official URL: http://www.sciencedirect.com/science/journal/00225193

View download statistics for this eprint

==>>> Export to other formats

Abstract

Many stochastic systems, including biological applications, use Markov chains in which there is a set of absorbing states. It is then needed to consider analogs of the stationary distribution of an irreducible chain. In this context, quasi-stationary distributions play a fundamental role to describe the long-term behavior of the system. The rationale for using quasi-stationary distribution is well established in the abundant existing literature. The aim of this study is to reformulate the ratio of means approach (Darroch and Seneta, 1965, 1967) which provides a simple alternative. We have a two-fold objective. The first objective is viewing quasi-stationarity and ratio of expectations as two different approaches for understanding the dynamics of the system before absorption. At this point, we remark that the quasi-stationary distribution and a ratio of means distribution may give or not give similar information. In this way, we arrive to the second objective; namely, to investigate the possibility of using the ratio of expectations distribution as an approximation to the quasi-stationary distribution. This second objective is explored by comparing both distributions in some selected scenarios, which are mainly inspired in stochastic epidemic models. Previously, the rate of convergence to the quasi-stationary regime is taking into account in order to make meaningful the comparison.

Item Type:Article
Uncontrolled Keywords:Stochastic logistic epidemic; Markov-chains; Death processes; Discrete-time; Extinction; Model; Sis; Birth; Populations; Subject; Quasi-stationarity; Ratio of expectations; Population models
Subjects:Sciences > Mathematics > Stochastic processes
ID Code:14966
Deposited On:24 Apr 2012 10:07
Last Modified:06 Feb 2014 10:13

Repository Staff Only: item control page