Mathematics · Markov Chains
Consider a Markov Chain X 0 , X 1 , X 2 , ... with state space S. Suppose i, j ∈ S are two states which communicate with each other. Which of the following statements is NOT correct?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Period of i = period of j
- 2i is recurrent if and only if j is recurrent
- 3lim n → ∞ P(X n = i | X 0 = k) = lim n → ∞ P(X n = j | X 0 = k) for all k ∞ S✓
- 4lim n → ∞ P(X n = j | X 0 = i) = lim n → ∞ P(X n = j | X 0 = j)
Correct answer
lim n → ∞ P(X n = i | X 0 = k) = lim n → ∞ P(X n = j | X 0 = k) for all k ∞ S
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