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Let be the following homogeneous Markovian chain with three state:

\begin{pmatrix} 1/2 & 1/4 & 1/4 \\ 2/3 & 0 & 1/3\\ 3/5 & 1/5 & 1/5 \end{pmatrix}

Is this Markovian chain irreducible?

From wikipedia:

A Markov chain is said to be irreducible if its state space is a single communicating class; in other words, if it is possible to get to any state from any state.

But here, there is no recursive path from 2 to 2, my answer would be no, but is it true?

Revolucion for Monica
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1 Answers1

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It is irreducible by the wiki definition. You can go 2 -> 1 -> 2.

Josef Ondrej
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