<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>117</id>
    <completedYear>2017</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>63</pageFirst>
    <pageLast>87</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>5</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2017-01-10</completedDate>
    <publishedDate>2017-01-10</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">(Sub-) Gradient formulae for probability functions of random inequality systems under Gaussian distribution</title>
    <abstract language="eng">We consider probability functions of parameter-dependent random inequality systems under&#13;
Gaussian distribution. As a main result, we provide an upper estimate for the Clarke subdifferential&#13;
of such probability functions without imposing compactness conditions. A constraint qualification&#13;
ensuring continuous differentiability is formulated. Explicit formulae are derived from the general&#13;
result in case of linear random inequality systems. In the case of a constant coefficient matrix an&#13;
upper estimate for even the smaller Mordukhovich subdifferential is proven.</abstract>
    <parentTitle language="eng">SIAM/ASA J. Uncertainty Quantification</parentTitle>
    <identifier type="doi">10.1137/16M1061308</identifier>
    <enrichment key="review.accepted_by">2</enrichment>
    <enrichment key="SubmissionStatus">published</enrichment>
    <author>Wim van Ackooij</author>
    <author>Rene Henrion</author>
    <collection role="institutes" number="">Weierstraß-Institut für Angewandte Analysis und Stochastik</collection>
    <collection role="subprojects" number="">B04</collection>
  </doc>
</export-example>
