Towards sample path estimates for fast–slow stochastic partial differential equations

Manuel V. Gnann, Christian Kuehn, Anne Pein

Research output: Contribution to journalArticleScientificpeer-review


Estimates for sample paths of fast–slow stochastic ordinary differential equations have become a key mathematical tool relevant for theory and applications. In particular, there have been breakthroughs by Berglund and Gentz to prove sharp exponential error estimates. In this paper, we take the first steps in order to generalise this theory to fast–slow stochastic partial differential equations. In a simplified setting with a natural decomposition into low- and high-frequency modes, we demonstrate that for a short-time period the probability for the corresponding sample path to leave a neighbourhood around the stable slow manifold of the system is exponentially small as well.
Original languageEnglish
Pages (from-to)1004-1024
Number of pages21
JournalEuropean Journal of Applied Mathematics
Issue number5
Publication statusPublished - Oct 2019
Externally publishedYes


  • Fast-slow system
  • stochastic partial differential equation
  • sample path
  • covariance neighborhood

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