Revision as of 02:33, 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...")
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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?