摘要
In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equation. We investigate this problem invoking two differen t met hods, respectively, based on variance compu tations and on pat h-wise considerations in Besov spaces. We are going to see that, as anticipated, both approaches lead to the same necessary and sufficient condition on the noise. In addition, the path-wise approach brings out regularity results for the solution.
In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equation. We investigate this problem invoking two different methods, respectively, based on variance computations and on path-wise considerations in Besov spaces. We are going to see that, as anticipated, both approaches lead to the same necessary and sufficient condition on the noise. In addition, the path-wise approach brings out regularity results for the solution.
作者
Yaozhong HU
Yanghui LIU
胡耀忠;刘阳辉;Samy TINDEL(Department of Mathematical and Statistical Sciences,University of Alberta,Edmonton,T6G 2G1,Canada;Department of Mathematics,Purdue University,West Lafayette,IN 47907,USA)
基金
supported by an NSERC grant
a startup fund of University of Alberta
supported by the NSF grant DMS1613163
