Counterexample

Is this true?

A recurrent chain has a stationary distribution

No — it is false.

The counterexample

The object that kills this claim comes with Trap Analysis.

86 counterexamples are free — including most of the ones Part C leans on hardest.

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Hypothesis dropped

A theorem applied without checking one of its preconditions.

See real exam options built on this mistake Drill statements like this

probability markov

Go deeper· Explained in full in Markov chains: classification and stationary behaviour· Asked in CSIR NET December 2025· From Limit Theorems and Markov Chains › Markov chains: classification of states, stationary distributions

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