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  <doc>
    <id>7983</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>379</pageFirst>
    <pageLast>403</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>20</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
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    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Approximative Policy Iteration for Exit Time Feedback Control Problems driven by Stochastic Differential Equations using Tensor Train format</title>
    <abstract language="eng">We consider a stochastic optimal exit time feedback control problem. The Bellman equation is solved approximatively via the Policy Iteration algorithm on a polynomial ansatz space by a sequence of linear equations. As high degree multi-polynomials are needed, the corresponding equations suffer from the curse of dimensionality even in moderate dimensions. We employ tensor-train methods to account for this problem. The approximation process within the Policy Iteration is done via a Least-Squares ansatz and the integration is done via Monte-Carlo methods. Numerical evidences are given for the (multi dimensional) double well potential and a three-hole potential.</abstract>
    <parentTitle language="eng">SIAM Journal on Multiscale Modeling and Simulation</parentTitle>
    <identifier type="arxiv">2010.04465</identifier>
    <identifier type="doi">10.1137/20M1372500</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Konstantin Fackeldey</author>
    <submitter>Konstantin Fackeldey</submitter>
    <author>Mathias Oster</author>
    <author>Leon Sallandt</author>
    <author>Reinhold Schneider</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="fackeldey">Fackeldey, Konstantin</collection>
    <collection role="projects" number="no-project">no-project</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
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