exercise:72dca0d567: Difference between revisions
From Stochiki
(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> Let <math>\mat{P}</math> be the transition matrix of an <math>r</math>-state ergodic chain. Prove that, if the diagonal entries <math>p_{ii}</math> are positive, then the chain is regular.") |
No edit summary |
||
| Line 5: | Line 5: | ||
\newcommand{\secstoprocess}{\all} | \newcommand{\secstoprocess}{\all} | ||
\newcommand{\NA}{{\rm NA}} | \newcommand{\NA}{{\rm NA}} | ||
\newcommand{\mathds}{\mathbb}</math></div> Let <math>\mat{P}</math> be the transition matrix of an <math>r</math>-state | \newcommand{\mathds}{\mathbb}</math></div> Let <math>\mat{P}</math> be the transition matrix of an <math>r</math>-state ergodic chain. Prove that, if the diagonal entries <math>p_{ii}</math> are positive, then the chain is regular. | ||
ergodic chain. Prove that, if the diagonal entries <math>p_{ii}</math> are positive, then | |||
the chain is regular. | |||
Latest revision as of 23:03, 17 June 2024
[math]
\newcommand{\NA}{{\rm NA}}
\newcommand{\mat}[1]{{\bf#1}}
\newcommand{\exref}[1]{\ref{##1}}
\newcommand{\secstoprocess}{\all}
\newcommand{\NA}{{\rm NA}}
\newcommand{\mathds}{\mathbb}[/math]
Let [math]\mat{P}[/math] be the transition matrix of an [math]r[/math]-state ergodic chain. Prove that, if the diagonal entries [math]p_{ii}[/math] are positive, then the chain is regular.