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 611, 2010 
Issue:

2010 
Year:


Pages:

107112 
. 
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:

20150708T06:51:52Z 
Last updated:

20150708 
Stable URL:

http://hdl.handle.net/10338.dmlcz/702747 
. 