Mathematics · Markov Chains
Let n ≥ 2 be a positive integer. Consider a Markov chain on the state space {1, 2, …, n} with a given transition probability matrix P. Let In denote the identity matrix of order n. Which of the following statements is necessarily true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1At least one state is recurrent.✓
- 2At least one state is transient.
- 3−13In + 43P is also a transition probability matrix of some Markov chain.
- 45 is an eigenvalue of In + 3P + P2.
Correct answer
At least one state is recurrent.
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