Description

• Title:
  On the Equivalence of Solutions for a Class of Stochastic Evolution Equations in a Banach Space
• Creator:
  Górajski, Mariusz
• Contributor:
  University of Łódź, Faculty of Economics and Sociology, Department of Econometrics;
  mariuszg@math.uni.lodz.pl
• Description:
  Acknowledgments: The author wishes to thank Professor Anna Chojnowska-Michalik and the referee for many helpful suggestions and comments.;
  We 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.
• Object availability:
  free access
• Rights:
  Uznanie autorstwa 3.0 Polska;
  http://creativecommons.org/licenses/by/3.0/pl
• Date:
  2015.08.18;
  2014.02.05
• Type:
  Article
• Language:
  English
• Format:
  application/pdf
• Publisher:
  Springer Basel
• Relation:
  Integral Equations and Operator Theory;;
  Integral Equations and Operator Theory;78
• Subject:
  Stochastic evolution equations, umd − Banach spaces;
  mild solutions;
  weak solutions;
  generalised strong solutions;
  stochastic partial differential equations with finite delay
• Identifier:
  1420-8989;
  http://hdl.handle.net/11089/11527 ;
  10.1007/s00020-013-2119-4
• Data provider:
  Repozytorium Uniwersytetu Łódzkiego
• Can I use it?:
  check license
• Type:
  image