dc.creator | Dietert, Helge | |

dc.date.accessioned | 2018-11-24T23:26:24Z | |

dc.date.available | 2015-05-27T09:05:20Z | |

dc.date.available | 2018-11-24T23:26:24Z | |

dc.date.issued | 2015-03-29 | |

dc.identifier | https://www.repository.cam.ac.uk/handle/1810/248009 | |

dc.identifier.uri | http://repository.aust.edu.ng/xmlui/handle/123456789/3820 | |

dc.description.abstract | In his 2011 work, Maas has shown that the law of any time-reversible continuoustime
Markov chain with finite state space evolves like a gradient flow of the relative
entropy with respect to its stationary distribution. In this work we show the converse
to the above by showing that if the relative law of a Markov chain with finite state
space evolves like a gradient flow of the relative entropy functional, it must be timereversible.
When we allow general functionals in place of the relative entropy, we show
that the law of a Markov chain evolves as gradient flow if and only if the generator
of the Markov chain is real diagonalisable. Finally, we discuss what aspects of the
functional are uniquely determined by the Markov chain. | |

dc.language | en | |

dc.publisher | Institute of Mathematical Statistics | |

dc.publisher | Electronic Communications in Probability | |

dc.rights | http://creativecommons.org/licenses/by/2.0/uk/ | |

dc.rights | Attribution 2.0 UK: England & Wales | |

dc.subject | Gradient flows | |

dc.subject | Finite state Markov chains | |

dc.subject | Time-reversibility | |

dc.title | Characterisation of gradient flows on finite state Markov chains | |

dc.type | Article | |