@article{KellerRoellyValleriani2015,
  author    = {Keller, Peter and Roelly, Sylvie and Valleriani, Angelo},
  title     = {On time duality for Markov Chains},
  series = {Stochastic models},
  volume    = {31},
  journal   = {Stochastic models},
  number    = {1},
  publisher = {Taylor \& Francis Group},
  address   = {Philadelphia},
  issn      = {1532-6349},
  doi       = {10.1080/15326349.2014.969736},
  pages     = {98 -- 118},
  year      = {2015},
  abstract  = {For an irreducible continuous time Markov chain, we derive the distribution of the first passage time from a given state i to another given state j and the reversed passage time from j to i, each under the condition of no return to the starting point. When these two distributions are identical, we say that i and j are in time duality. We introduce a new condition called permuted balance that generalizes the concept of reversibility and provides sufficient criteria, based on the structure of the transition graph of the Markov chain. Illustrative examples are provided.},
  language  = {en}
}