| Title:
|
On convergence of homogeneous Markov chains (English) |
| Author:
|
Kratochvíl, Petr |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
28 |
| Issue:
|
2 |
| Year:
|
1983 |
| Pages:
|
116-119 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $p_t$ be a vector of absolute distributions of probabilities in an irreducible aperiodic homogeneous Markov chain with a finite state space. Professor Alladi Ramakrishnan conjectured the following strict inequality for norms of differences $\left\|p_{t+2}-p_{t+1}\right\|<\left\|p_{t+1}-p_t\right\|$. In the paper, a necessary and sufficient condition for the validity of this inequality is proved, which may be useful in investigating the character of convergence of distributions in Markov chains. (English) |
| Keyword:
|
convergence of distributions |
| MSC:
|
60J10 |
| idZBL:
|
Zbl 0511.60065 |
| idMR:
|
MR0695185 |
| DOI:
|
10.21136/AM.1983.104012 |
| . |
| Date available:
|
2008-05-20T18:21:31Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104012 |
| . |
