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Short answer: don't.

Don't.

In fact, one never shows that a state is absorbing through Borel-Cantelli lemma. Or that a state is recurrent, since this would mean using the part of Borel-Cantelli lemma where a series diverges, which needs independence, and the successive times of visits of a given state by a Markov chain are hardly independent.

Short answer: don't.

In fact, one never shows that a state is absorbing through Borel-Cantelli lemma. Or that a state is recurrent, since this would mean using the part of Borel-Cantelli lemma where a series diverges, which needs independence, and the successive times of visits of a given state by a Markov chain are hardly independent.

Short answer:

Don't.

In fact, one never shows that a state is absorbing through Borel-Cantelli lemma. Or that a state is recurrent, since this would mean using the part of Borel-Cantelli lemma where a series diverges, which needs independence, and the successive times of visits of a given state by a Markov chain are hardly independent.

Source Link
Did
Did
  • 5.7k
  • 1
  • 30
  • 36

Short answer: don't.

In fact, one never shows that a state is absorbing through Borel-Cantelli lemma. Or that a state is recurrent, since this would mean using the part of Borel-Cantelli lemma where a series diverges, which needs independence, and the successive times of visits of a given state by a Markov chain are hardly independent.