Insensitivity analysis of Markov chains

Kocurek, Martin. "Insensitivity analysis of Markov chains." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics AS CR, 2010. 107-112. <http://eudml.org/doc/271330>.

@inProceedings{Kocurek2010,
abstract = {Sensitivity analysis of irreducible Markov chains considers an original Markov chain with transition probability matrix $P$ and modified Markov chain with transition probability matrix $P$. For their respective stationary probability vectors $\pi , \tilde\{\pi \}$, some of the following charactristics are usually studied: $\Vert \pi - \tilde\{\pi \}\Vert _p$ for asymptotical stability [3], $|\pi _i- \tilde\{\pi \}_i|, \frac\{|\pi _i- \tilde\{\pi \}_i|\}\{\pi _i\}$ for componentwise stability or sensitivity [1]. For functional transition probabilities, $P=P(t)$ and stationary probability vector $\pi (t)$, derivatives are also used for studying sensitivity of some components of stationary distribution with respect to modifications of $P$ [2]. In special cases, modifications of matrix $P$ leave certain stationary probabilities unchanged. This paper studies some special cases which lead to this behavior of stationary probabilities.},
author = {Kocurek, Martin},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {Markov chain; finite irreducible Markov chain; sensitivity analysis; stationary probability; transition probability; lumpability},
location = {Prague},
pages = {107-112},
publisher = {Institute of Mathematics AS CR},
title = {Insensitivity analysis of Markov chains},
url = {http://eudml.org/doc/271330},
year = {2010},
}

TY - CLSWK
AU - Kocurek, Martin
TI - Insensitivity analysis of Markov chains
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2010
CY - Prague
PB - Institute of Mathematics AS CR
SP - 107
EP - 112
AB - Sensitivity analysis of irreducible Markov chains considers an original Markov chain with transition probability matrix $P$ and modified Markov chain with transition probability matrix $P$. For their respective stationary probability vectors $\pi , \tilde{\pi }$, some of the following charactristics are usually studied: $\Vert \pi - \tilde{\pi }\Vert _p$ for asymptotical stability [3], $|\pi _i- \tilde{\pi }_i|, \frac{|\pi _i- \tilde{\pi }_i|}{\pi _i}$ for componentwise stability or sensitivity [1]. For functional transition probabilities, $P=P(t)$ and stationary probability vector $\pi (t)$, derivatives are also used for studying sensitivity of some components of stationary distribution with respect to modifications of $P$ [2]. In special cases, modifications of matrix $P$ leave certain stationary probabilities unchanged. This paper studies some special cases which lead to this behavior of stationary probabilities.
KW - Markov chain; finite irreducible Markov chain; sensitivity analysis; stationary probability; transition probability; lumpability
UR - http://eudml.org/doc/271330
ER -