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मार्कोव श्रृंखला X0, X1, X2, .... पर विचार करें जिसकी अवस्था समष्ठि S है।

i, j ∈ S दो ऐसी अवस्थायें हैं जो एक दूसरे के साथ संपर्क करती हैं। निम्न में से कौन सा वक्तव्य सत्य नहीं है?

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CSIR-UGC (NET) Mathematical Science: Held on (26 Nov 2020)
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  1. i का 'पीरियड = j का 'पीरियड'
  2. i पुनरावर्ती है यदि और केवल यदि j पुनरावर्ती है
  3. \(\lim _{n \rightarrow \infty}\) P(Xn = i | X0 = k) = \(\lim _{n \rightarrow \infty}\) P(Xn = j | X0 = k) सभी k ∈ S के लिए
  4. \(\lim _{n \rightarrow \infty}\) P(Xn = j | X0 = i) = \(\lim _{n \rightarrow \infty}\) P(Xn = j | X0 = j)

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Option 3 : \(\lim _{n \rightarrow \infty}\) P(Xn = i | X0 = k) = \(\lim _{n \rightarrow \infty}\) P(Xn = j | X0 = k) सभी k ∈ S के लिए
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Q2.मार्कोव श्रृंखला X0, X1, X2, .... पर विचार करें जिसकी अवस्था समष्ठि S है। i, j ∈ S दो ऐसी अवस्थायें हैं जो एक दूसरे के साथ संपर्क करती हैं। निम्न में से कौन सा वक्तव्य सत्य नहीं है?

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