An Efficient Procedure for Computing Quasi-Stationary Distributions of Markov Chains with Sparse Transition Structure
P. Pollett, and D. Stewart. Advances in Applied Probability, 26 (1):
pp. 68-79(1994)
Abstract
We describe a computational procedure for evaluating the quasi-stationary distributions of a continuous-time Markov chain. Our method, which is an 'iterative version' of Arnoldi's algorithm, is appropriate for dealing with cases where the matrix of transition rates is large and sparse, but does not exhibit a banded structure which might otherwise be usefully exploited. We illustrate the method with reference to an epidemic model and we compare the computed quasi-stationary distribution with an appropriate diffusion approximation.
%0 Journal Article
%1 pollett1994efficient
%A Pollett, P. K.
%A Stewart, D. E.
%D 1994
%I Applied Probability Trust
%J Advances in Applied Probability
%K Arnoldi_algorithm Krylov_methods Markov_chain numerical_methods quasistationarity sparse_matrix
%N 1
%P pp. 68-79
%T An Efficient Procedure for Computing Quasi-Stationary Distributions of Markov Chains with Sparse Transition Structure
%U http://www.jstor.org/stable/1427580
%V 26
%X We describe a computational procedure for evaluating the quasi-stationary distributions of a continuous-time Markov chain. Our method, which is an 'iterative version' of Arnoldi's algorithm, is appropriate for dealing with cases where the matrix of transition rates is large and sparse, but does not exhibit a banded structure which might otherwise be usefully exploited. We illustrate the method with reference to an epidemic model and we compare the computed quasi-stationary distribution with an appropriate diffusion approximation.
@article{pollett1994efficient,
abstract = {We describe a computational procedure for evaluating the quasi-stationary distributions of a continuous-time Markov chain. Our method, which is an 'iterative version' of Arnoldi's algorithm, is appropriate for dealing with cases where the matrix of transition rates is large and sparse, but does not exhibit a banded structure which might otherwise be usefully exploited. We illustrate the method with reference to an epidemic model and we compare the computed quasi-stationary distribution with an appropriate diffusion approximation.},
added-at = {2013-03-27T15:10:30.000+0100},
author = {Pollett, P. K. and Stewart, D. E.},
biburl = {https://www.bibsonomy.org/bibtex/2c5b84ae02cffaa8ea1b1289166b9a622/peter.ralph},
interhash = {4c0c899e1fab77e6fbfac6e5afcd157a},
intrahash = {c5b84ae02cffaa8ea1b1289166b9a622},
issn = {00018678},
journal = {Advances in Applied Probability},
jstor_articletype = {research-article},
jstor_formatteddate = {Mar., 1994},
keywords = {Arnoldi_algorithm Krylov_methods Markov_chain numerical_methods quasistationarity sparse_matrix},
language = {English},
number = 1,
pages = {pp. 68-79},
publisher = {Applied Probability Trust},
timestamp = {2013-03-27T15:11:05.000+0100},
title = {An Efficient Procedure for Computing Quasi-Stationary Distributions of {Markov} Chains with Sparse Transition Structure},
url = {http://www.jstor.org/stable/1427580},
volume = 26,
year = 1994
}