Kelly's lemma

In probability theory, Kelly's lemma states that for a stationary continuous-time Markov chain, a process defined as the time-reversed process has the same stationary distribution as the forward-time process.[1] The theorem is named after Frank Kelly.[2][3][4][5]

  1. ^ Boucherie, Richard J.; van Dijk, N. M. (2011). Queueing Networks: A Fundamental Approach. Springer. p. 222. ISBN 144196472X.
  2. ^ Kelly, Frank P. (1979). Reversibility and Stochastic Networks. J. Wiley. p. 22. ISBN 0471276014.
  3. ^ Walrand, Jean (1988). An introduction to queueing networks. Prentice Hall. p. 63 (Lemma 2.8.5). ISBN 013474487X.
  4. ^ Kelly, F. P. (1976). "Networks of Queues". Advances in Applied Probability. 8 (2): 416–432. doi:10.2307/1425912. JSTOR 1425912.
  5. ^ Asmussen, S. R. (2003). "Markov Jump Processes". Applied Probability and Queues. Stochastic Modelling and Applied Probability. Vol. 51. pp. 39–59. doi:10.1007/0-387-21525-5_2. ISBN 978-0-387-00211-8.