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  • 标题:Absolute continuity for SPDEs with irregular fundamental solution
  • 本地全文:下载
  • 作者:Sanz-Solé, Marta ; Süss, André
  • 期刊名称:Electronic Communications in Probability
  • 印刷版ISSN:1083-589X
  • 出版年度:2015
  • 卷号:20
  • 期号:0
  • 页码:1-11
  • DOI:10.1214/ECP.v20-3831
  • 语种:English
  • 出版社:Electronic Communications in Probability
  • 摘要:For a class of stochastic partial differential equations studied by Conus and Dalang, we prove the existence of density of the probability law of the solution at a given point $(t,x)$, and that the density belongs to some Besov space. The proof relies on a method developed by Debussche and Romito.The result can be applied to the solution of the stochastic wave equation with multiplicative noise, Lipschitz coefficients and any spatial dimension $d\ge 1$, and also to the heat equation.This provides an extension of earlier results.
  • 关键词:Stochastic partial differential equations; stochastic wave equation; densities.;Primary 60H15; 60H07; Secondary 60H20; 60H05.
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