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# The Exit Time Finite State Projection Scheme: Bounding Exit Distributions and Occupation Measures of Continuous-Time Markov Chains Read More: https://epubs.siam.org/doi/10.1137/18M1168261

Kuntz, Juan; Thomas, Philipp; Stan, Guy-Bart; Barahona, Mauricio

### DataCite XML Export

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<identifier identifierType="DOI">10.5281/zenodo.2668385</identifier>
<creators>
<creator>
<creatorName>Kuntz, Juan</creatorName>
<givenName>Juan</givenName>
<familyName>Kuntz</familyName>
<nameIdentifier nameIdentifierScheme="ORCID" schemeURI="http://orcid.org/">0000-0002-5855-6074</nameIdentifier>
<affiliation>Department of Mathematics and Department of Bioengineering, Imperial College London, London, SW7 2AZ, UK</affiliation>
</creator>
<creator>
<creatorName>Thomas, Philipp</creatorName>
<givenName>Philipp</givenName>
<familyName>Thomas</familyName>
<nameIdentifier nameIdentifierScheme="ORCID" schemeURI="http://orcid.org/">0000-0003-4919-8452</nameIdentifier>
<affiliation>Department of Mathematics, Imperial College London, London, SW7 2AZ, UK</affiliation>
</creator>
<creator>
<creatorName>Stan, Guy-Bart</creatorName>
<givenName>Guy-Bart</givenName>
<familyName>Stan</familyName>
<nameIdentifier nameIdentifierScheme="ORCID" schemeURI="http://orcid.org/">0000-0002-5560-902X</nameIdentifier>
<affiliation>Department of Bioengineering, Imperial College London, London, SW7 2AZ, UK</affiliation>
</creator>
<creator>
<creatorName>Barahona, Mauricio</creatorName>
<givenName>Mauricio</givenName>
<familyName>Barahona</familyName>
<nameIdentifier nameIdentifierScheme="ORCID" schemeURI="http://orcid.org/">0000-0002-1089-5675</nameIdentifier>
<affiliation>Department of Mathematics, Imperial College London, London, SW7 2AZ, UK</affiliation>
</creator>
</creators>
<titles>
<title>The Exit Time Finite State Projection Scheme: Bounding Exit Distributions and Occupation Measures of Continuous-Time Markov Chains   Read More: https://epubs.siam.org/doi/10.1137/18M1168261</title>
</titles>
<publisher>Zenodo</publisher>
<publicationYear>2019</publicationYear>
<subjects>
<subject>Exit times</subject>
<subject>First passage times</subject>
<subject>Continuous-time Markov chains</subject>
<subject>Exit time finite state projection</subject>
<subject>Finite state projection</subject>
<subject>Exit distribution</subject>
<subject>Occupation measure</subject>
</subjects>
<dates>
<date dateType="Issued">2019-03-12</date>
</dates>
<language>en</language>
<resourceType resourceTypeGeneral="Text">Preprint</resourceType>
<alternateIdentifiers>
<alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/2668385</alternateIdentifier>
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<relatedIdentifiers>
<relatedIdentifier relatedIdentifierType="DOI" relationType="IsVersionOf">10.5281/zenodo.2668384</relatedIdentifier>
<relatedIdentifier relatedIdentifierType="URL" relationType="IsPartOf">https://zenodo.org/communities/cosy-bio</relatedIdentifier>
</relatedIdentifiers>
<rightsList>
<rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
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<descriptions>
<description descriptionType="Abstract">&lt;p&gt;&lt;strong&gt;Abstract&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;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.&lt;/p&gt;</description>
</descriptions>
<fundingReferences>
<fundingReference>
<funderName>European Commission</funderName>
<funderIdentifier funderIdentifierType="Crossref Funder ID">10.13039/501100000780</funderIdentifier>
<awardNumber awardURI="info:eu-repo/grantAgreement/EC/H2020/766840/">766840</awardNumber>
<awardTitle>Control Engineering of Biological Systems for Reliable Synthetic Biology Applications</awardTitle>
</fundingReference>
</fundingReferences>
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