# Article

 Title: Insensitivity analysis of Markov chains (English) Author: Kocurek, Martin Language: English Journal: Programs and Algorithms of Numerical Mathematics Volume: Proceedings of Seminar. Dolní Maxov, June 6-11, 2010 Issue: 2010 Year: Pages: 107-112 . Category: math . Summary: 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: $\|\pi - \tilde{\pi}\|_p$ 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. (English) Keyword: Markov chain Keyword: finite irreducible Markov chain Keyword: sensitivity analysis Keyword: stationary probability Keyword: transition probability Keyword: lumpability MSC: 60J10 MSC: 60J35 . Date available: 2015-07-08T06:51:52Z Last updated: 2015-07-08 Stable URL: http://hdl.handle.net/10338.dmlcz/702747 .

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