TOTAL VARIATION APPROXIMATION FOR QUASI-STATIONARY DISTRIBUTIONS

被引：15

作者：

Barbour, A. D. ^{[1
]}

Pollett, P. K. ^{[2
]}

机构：

[1] Univ Zurich, CH-8057 Zurich, Switzerland

[2] Univ Queensland, Dept Math, Brisbane, Qld 4072, Australia

来源：

JOURNAL OF APPLIED PROBABILITY | 2010年 / 47卷 / 04期

基金：

澳大利亚研究理事会;

关键词：

Quasi-stationary distribution; total variation distance; stochastic logistic model; CONVERGENCE;

D O I：

10.1239/jap/1294170510

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Quasi-stationary distributions, as discussed in Darroch and Seneta (1965), have been used in biology to describe the steady state behaviour of population models which, while eventually certain to become extinct, nevertheless maintain an apparent stochastic equilibrium for long periods. These distributions have some drawbacks: they need not exist, nor be unique, and their calculation can present problems. In this paper, we give biologically plausible conditions under which the quasi-stationary distribution is unique, and can be closely approximated by distributions that are simple to compute.

引用

页码：934 / 946

页数：13

共 13 条

[1]

Anderson W., 1991, CONTINUOUS TIME MARK, DOI 10.1007/978-1-4612-3038-0

[2]

Bartlett M.S., 1960, Stochastic Population Models in Ecology and Epidemiology

[3] QUASI-STATIONARY DISTRIBUTIONS AND DIFFUSION MODELS IN POPULATION DYNAMICS [J].