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

被引：0
|
作者：
Mariusz Górajski
机构：
[1] University of Łódź,Department of Econometrics, Faculty of Economics and Sociology
来源：
Integral Equations and Operator Theory | 2014年 / 78卷
关键词：
Primary 34K50; Secondary 60H30; 47D06; Stochastic evolution equations; Banach spaces; mild solutions; weak solutions; generalised strong solutions; stochastic partial differential equations with finite delay;
D O I：
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学科分类号：
摘要：
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.
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页码：451 / 481
页数：30
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