A distribution is an invariant distribution when
(1)
for every state . The pair satisfies detailed balance when
(2)
for every . Summing this identity over gives
(3)
so detailed balance implies invariance.
For an irreducible positive recurrent Markov chain, Kac's lemma relates the invariant mass to the mean recurrence time:
(4)

Ancestors (12)

  1. i
  2. a
  3. 18H
  4. Paper 2
  5. ib
  6. 2021
  7. Past exam of the mathematics course of the University of Cambridge
  8. Mathematics course of the University of Cambridge
  9. Course of the University of Cambridge
  10. University of Cambridge
  11. List of universities
  12. Home

View article source

Discussion (0)

New discussion

There are no discussions about this article yet.

Articles by others on the same topic (0)

There are currently no matching articles.
See all articles in the same topic Create my own version