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The high-dimensional integrals are computed numerically using specially designed QMC methods and, under moderate assumptions on the input random field, the error rate is shown to be essentially linear, independently of the stochastic dimension of the problem\u2014and thereby superior to ordinary Monte Carlo methods. Numerical results demonstrate the effectiveness of our method.<\/jats:p>","DOI":"10.1007\/s00211-024-01397-9","type":"journal-article","created":{"date-parts":[[2024,3,11]],"date-time":"2024-03-11T13:03:02Z","timestamp":1710162182000},"page":"565-608","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Parabolic PDE-constrained optimal control under uncertainty with entropic risk measure using quasi-Monte Carlo integration"],"prefix":"10.1007","volume":"156","author":[{"given":"Philipp A.","family":"Guth","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vesa","family":"Kaarnioja","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Frances Y.","family":"Kuo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Claudia","family":"Schillings","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ian H.","family":"Sloan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,3,11]]},"reference":[{"key":"1397_CR1","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1111\/1467-9965.00068","volume":"9","author":"P Artzner","year":"2001","unstructured":"Artzner, P., Delbaen, F., Eber, J.M., Heath, D.: Coherent measures of risk. 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