| 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 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: $\|\pi - \tilde{\pi}\|_p$ 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:
|
2023-06-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/702747 |
| . |
