Sensitivity analysis of irreducible Markov chains considers an original Markov chain with transition probability matix $P$ 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: $\parallel \pi -\tilde{\pi }{\parallel }_p$ 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, $P=P\left(t\right)$ and stationary probability vector $\pi \left(t\right)$, 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.

EUDML-ID : urn:eudml:doc:271330
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Mots clés:

@article{702747,
     title = {Insensitivity analysis of Markov chains},
     booktitle = {Programs and Algorithms of Numerical Mathematics},
     series = {GDML\_Books},
     publisher = {Institute of Mathematics AS CR},
     address = {Prague},
     year = {2010},
     pages = {107-112},
     url = {http://dml.mathdoc.fr/item/702747}
}

Kocurek, Martin. Insensitivity analysis of Markov chains, dans Programs and Algorithms of Numerical Mathematics, GDML_Books,  (2010), pp. 107-112. http://gdmltest.u-ga.fr/item/702747/