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Covariance structure of parabolic stochastic partial differential equations

by A. Lang and S. Larsson and Ch. Schwab

(Report number 2012-32)

Abstract
In this paper parabolic random partial differential equations and parabolic stochastic partial differential equations driven by a Wiener process are considered. A deterministic, tensorized evolution equation for the second moment and the covariance of the solutions of the parabolic stochastic partial differential equations is derived. Well-posedness of a space-time weak variational formulation of this tensorized equation is established.

Keywords:

@Techreport{LLS12_475,
  author = {A. Lang and S. Larsson and Ch. Schwab},
  title = {Covariance structure of parabolic stochastic partial differential equations},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2012-32},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2012/2012-32.pdf },
  year = {2012}
}

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