Structural Properties of Finite Markov Processes 

Find the communicating classes, highlighted in the graph through different colors.

In[1]:=

X proc = DiscreteMarkovProcess[ 1, {{0, 1/3, 0, 2/3, 0}, {1/2, 0, 0, 0, 1/2}, {0, 0, 1/2, 1/2, 0}, {0, 0, 1/2, 1/2, 0}, {0, 0, 0, 0, 1}}];

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X gr = Graph[proc, GraphLayout -> "LayeredDrawing"]

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In[3]:=

X MarkovProcessProperties[proc, "CommunicatingClasses"]

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Check for irreducibility, which means there is only one communicating class.

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X MarkovProcessProperties[proc, "Irreducible"]

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Find the recurrent classes, which are classes that cannot be exited.

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X MarkovProcessProperties[proc, "RecurrentClasses"]

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Find the transient classes, which are classes that can be exited.

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X MarkovProcessProperties[proc, "TransientClasses"]

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Find the absorbing classes, which are recurrent classes with a single state.

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X MarkovProcessProperties[proc, "AbsorbingClasses"]

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