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On the Equivalence of Solutions for a Class of Stochastic Evolution Equations in a Banach Space

dc.contributor.authorGórajski, Mariusz
dc.date.accessioned2015-08-18T09:35:44Z
dc.date.available2015-08-18T09:35:44Z
dc.date.issued2014-02-05
dc.identifier.issn1420-8989
dc.identifier.urihttp://hdl.handle.net/11089/11527
dc.descriptionAcknowledgments: The author wishes to thank Professor Anna Chojnowska-Michalik and the referee for many helpful suggestions and comments.pl_PL
dc.description.abstractWe study a class of stochastic evolution equations in a Banach space E driven by cylindrical Wiener process. Three different analytical concepts of solutions: generalised strong, weak and mild are defined and the conditions under which they are equivalent are given. We apply this result to prove existence, uniqueness and continuity of weak solutions to stochastic delay evolution equations. We also consider two examples of these equations in non-reflexive Banach spaces: a stochastic transport equation with delay and a stochastic delay McKendrick equation.pl_PL
dc.language.isoenpl_PL
dc.publisherSpringer Baselpl_PL
dc.relation.ispartofseriesIntegral Equations and Operator Theory;
dc.relation.ispartofseriesIntegral Equations and Operator Theory;78
dc.rightsUznanie autorstwa 3.0 Polska*
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/pl/*
dc.subjectStochastic evolution equations, umd − Banach spacespl_PL
dc.subjectmild solutionspl_PL
dc.subjectweak solutionspl_PL
dc.subjectgeneralised strong solutionspl_PL
dc.subjectstochastic partial differential equations with finite delaypl_PL
dc.titleOn the Equivalence of Solutions for a Class of Stochastic Evolution Equations in a Banach Spacepl_PL
dc.typeArticlepl_PL
dc.page.number451–481pl_PL
dc.contributor.authorAffiliationUniversity of Łódź, Faculty of Economics and Sociology, Department of Econometricspl_PL
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dc.contributor.authorEmailmariuszg@math.uni.lodz.plpl_PL
dc.identifier.doi10.1007/s00020-013-2119-4


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