exercise:958c6ba2a8: 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> 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...") |
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\mat {P} = \pmatrix{ 1 - a & a \cr b & 1 - b}\ . | \mat {P} = \pmatrix{ 1 - a & a \cr b & 1 - b}\ . | ||
</math> | </math> | ||
<ul><li> Under what conditions is <math>\mat{P}</math> absorbing? | <ul style="list-style-type:lower-alpha"><li> Under what conditions is <math>\mat{P}</math> absorbing? | ||
</li> | </li> | ||
<li> Under what conditions is <math>\mat{P}</math> ergodic but not regular? | <li> Under what conditions is <math>\mat{P}</math> ergodic but not regular? | ||
Latest revision as of 22:46, 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]
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?