exercise:4c8e0e20c1: 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> Prove that if <math>\mat{P}</math> is the transition matrix of an ergodic chain, then <math>(1/2)(\mat {I} + \mat {P})</math> is the transition matrix of a regular chain. '' Hint'': Use Exercise Exercise.") |
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> Prove that if <math>\mat{P}</math> is the transition matrix of an | \newcommand{\mathds}{\mathbb}</math></div> Prove that if <math>\mat{P}</math> is the transition matrix of an ergodic chain, then <math>(1/2)(\mat {I} + \mat {P})</math> is the transition matrix of a regular chain. '' Hint'': Use [[exercise:72dca0d567 |Exercise]]. | ||
ergodic chain, then <math>(1/2)(\mat {I} + \mat {P})</math> is the transition matrix of a | |||
regular chain. '' Hint'': Use | |||
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]
Prove that if [math]\mat{P}[/math] is the transition matrix of an ergodic chain, then [math](1/2)(\mat {I} + \mat {P})[/math] is the transition matrix of a regular chain. Hint: Use Exercise.