### The exit time finite state projection scheme: bounding exit distributions and occupation measures of continuous-time Markov chains

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Kuntz_ETFSP.pdf | Accepted version | 3.31 MB | Adobe PDF | View/Open |

Title: | The exit time finite state projection scheme: bounding exit distributions and occupation measures of continuous-time Markov chains |

Authors: | Kuntz, J Thomas, P Stan, G-B Barahona, M |

Item Type: | Journal Article |

Abstract: | We introduce the exit time finite state projection (ETFSP) scheme, a truncation- based method that yields approximations to the exit distribution and occupation measure associated with the time of exit from a domain (i.e., the time of first passage to the complement of the domain) of time-homogeneous continuous-time Markov chains. We prove that: (i) the computed approximations bound the measures from below; (ii) the total variation distances between the approximations and the measures decrease monotonically as states are added to the truncation; and (iii) the scheme converges, in the sense that, as the truncation tends to the entire state space, the total variation distances tend to zero. Furthermore, we give a computable bound on the total variation distance between the exit distribution and its approximation, and we delineate the cases in which the bound is sharp. We also revisit the related finite state projection scheme and give a comprehensive account of its theoretical properties. We demonstrate the use of the ETFSP scheme by applying it to two biological examples: the computation of the first passage time associated with the expression of a gene, and the fixation times of competing species subject to demographic noise. |

Issue Date: | 12-Mar-2019 |

Date of Acceptance: | 23-Jan-2019 |

URI: | http://hdl.handle.net/10044/1/66083 |

DOI: | https://dx.doi.org/10.1137/18M1168261 |

ISSN: | 1064-8275 |

Publisher: | Society for Industrial and Applied Mathematics |

Start Page: | A748 |

End Page: | A769 |

Journal / Book Title: | SIAM Journal on Scientific Computing |

Volume: | 41 |

Issue: | 2 |

Copyright Statement: | © 2019 Society for Industrial and Applied Mathematics |

Sponsor/Funder: | Engineering & Physical Science Research Council (EPSRC) Engineering & Physical Science Research Council (EPSRC) |

Funder's Grant Number: | EP/I017267/1 EP/N014529/1 |

Keywords: | Science & Technology Physical Sciences Mathematics, Applied Mathematics exit times first passage times continuous-time Markov chains exit time finite state projection finite state projection exit distribution occupation measure CHEMICAL MASTER EQUATION COMPUTATION MOMENTS NOISE math.PR math.PR cond-mat.stat-mech math.OC q-bio.MN q-bio.PE 60J27, 60J28, 65C40, 65G20 math.PR math.PR cond-mat.stat-mech math.OC q-bio.MN q-bio.PE 60J27, 60J28, 65C40, 65G20 Numerical & Computational Mathematics 0102 Applied Mathematics 0103 Numerical and Computational Mathematics 0802 Computation Theory and Mathematics |

Publication Status: | Published |

Online Publication Date: | 2019-03-12 |

Appears in Collections: | Faculty of Engineering Bioengineering Mathematics Applied Mathematics and Mathematical Physics Faculty of Natural Sciences |