exercise:92521d1534: 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 transition matrix in Exercise \ref{exer 11.3.3}, with <math>a = b = 1</math>. Show that this chain is ergodic but not regular. Find the fixed probability vector and interpret it. Show that <math>\mat {P}^n</math>...") |
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\newcommand{\mathds}{\mathbb}</math></div> Consider the Markov chain with transition matrix in | \newcommand{\mathds}{\mathbb}</math></div> Consider the Markov chain with transition matrix in [[exercise:958c6ba2a8|Exercise]], with <math>a = b = 1</math>. Show that this chain is ergodic but not regular. | ||
Exercise | |||
Find the fixed probability vector and interpret it. Show that <math>\mat {P}^n</math> does not tend to a limit, but that | |||
Find the fixed | |||
probability vector and interpret it. Show that <math>\mat {P}^n</math> does not tend to a | |||
limit, but that | |||
<math display="block"> | <math display="block"> | ||
Latest revision as of 22:49, 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 transition matrix in Exercise, with [math]a = b = 1[/math]. Show that this chain is ergodic but not regular.
Find the fixed probability vector and interpret it. Show that [math]\mat {P}^n[/math] does not tend to a limit, but that
[[math]]
\mat {A}_n = \frac{\mat {I} + \mat {P} + \mat {P}^2 +\cdots + \mat {P}^n}{n +
1}
[[/math]]
does.