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MarkovProcessProperties bugs


Mathematica 9 appears to have this bug:

MarkovProcessProperties[
 DiscreteMarkovProcess[
  initVec, {{0, 1/2, 1/2, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {1, 0, 0, 
    0}} ], "Aperiodic"]

returns "False".  

However, the stochastic matrix {{0, 1/2, 1/2, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {1, 0, 0, 
    0}} is primitive, i.e. irreducible and aperiodic.  The positive diagonal entry 1/2 at [[2,2]] guarantees aperiodicity.

Similarly, "False" is returned on {{0, 1/2, 1/2, 0}, {1, 0, 0, 0}, {0, 0, 1/2, 1/2}, {1, 0, 0, 0}}

while "True" is returned on
{{0, 1/2, 1/2, 0}, {1/2, 1/2, 0, 0}, {0, 0, 1/2, 1/2}, {1, 0, 0, 0}} .

All of these examples, however, are aperiodic.



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