In this section
@article{Kuntz:2021,
author = {Kuntz, J and Thomas, P and Stan, G-B and Barahona, M},
journal = {SIAM Review},
title = {Stationary distributions of continuous-time Markov chains: a review of theory and truncation-based approximations},
url = {http://arxiv.org/abs/1909.05794v1},
year = {2021}
}
TY - JOUR
AB - Computing the stationary distributions of a continuous-time Markov chaininvolves solving a set of linear equations. In most cases of interest, thenumber of equations is infinite or too large, and cannot be solved analyticallyor numerically. Several approximation schemes overcome this issue by truncatingthe state space to a manageable size. In this review, we first give acomprehensive theoretical account of the stationary distributions and theirrelation to the long-term behaviour of the Markov chain, which is readilyaccessible to non-experts and free of irreducibility assumptions made instandard texts. We then review truncation-based approximation schemes payingparticular attention to their convergence and to the errors they introduce, andwe illustrate their performance with an example of a stochastic reactionnetwork of relevance in biology and chemistry. We conclude by elaborating oncomputational trade-offs associated with error control and some open questions.
AU - Kuntz,J
AU - Thomas,P
AU - Stan,G-B
AU - Barahona,M
PY - 2021///
SN - 0036-1445
TI - Stationary distributions of continuous-time Markov chains: a review of theory and truncation-based approximations
T2 - SIAM Review
UR - http://arxiv.org/abs/1909.05794v1
UR - http://hdl.handle.net/10044/1/81806
ER -