Revision as of 22:08, 17 June 2024 by Admin
BBy Bot
Jun 09'24
Exercise
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Let [math]\mat{P}[/math] be the transition matrix of an ergodic Markov chain. Let [math]\mat{w}[/math] be a fixed probability vector (i.e., [math]\mat{w}[/math] is a row vector with [math]\mat {w}\mat {P} = \mat {w}[/math]). Show that if [math]w_i = 0[/math] and [math]p_{ji} \gt 0[/math] then [math]w_j = 0[/math]. Use this to show that the fixed probability vector for an ergodic chain cannot have any 0 entries.