Stochastic mode-reduction in models with conservative fast sub-systems

Ankita Jain, Ilya Timofeyev, Eric Vanden-Eijnden

Research output: Contribution to journalArticlepeer-review


A stochastic mode reduction strategy is applied to multiscale models with a deterministic energy-conserving fast sub-system. Specifically, we consider situations where the slow variables are driven stochastically and interact with the fast sub-system in an energy-conserving fashion. Because the stochastic terms only affect the slow variables, the fast sub-system evolves deterministically on a sphere of constant energy. However, in the full model the radius of the sphere slowly changes due to the coupling between the slow and fast dynamics. Therefore, the energy of the fast sub-system becomes an additional hidden slow variable that must be accounted for in order to apply the stochastic mode reduction technique to systems of this type.

Original languageEnglish (US)
Pages (from-to)297-314
Number of pages18
JournalCommunications in Mathematical Sciences
Issue number2
StatePublished - 2015


  • Conservative fast sub-system
  • Mode-reduction

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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