Revision as of 03:33, 9 June 2024 by Bot (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> Consider the Markov chain with general <math>2 \times 2</math> transition matrix <math display="block"> \mat {P} = \pmatrix{ 1 - a & a \cr b & 1 - b}\ . </math> <ul><li> Under what conditions is <math>\mat{P}</math> absorbing? </li> <li> Under wh...")
BBy Bot
Jun 09'24
Exercise
[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]
Consider the Markov chain with general [math]2 \times 2[/math]
transition matrix
[[math]]
\mat {P} = \pmatrix{ 1 - a & a \cr b & 1 - b}\ .
[[/math]]
- Under what conditions is [math]\mat{P}[/math] absorbing?
- Under what conditions is [math]\mat{P}[/math] ergodic but not regular?
- Under what conditions is [math]\mat{P}[/math] regular?