exercise:72dca0d567: Difference between revisions

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(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.")
 
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\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 22:03, 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.