On Cameron-Martin theorem and almost sure global existence

Tadahiro Oh, Jeremy Quastel

Research output: Contribution to journalArticlepeer-review


n this note, we discuss various aspects of invariant measures for nonlinear Hamiltonian PDEs. In particular, we show almost sure global existence for some Hamiltonian PDEs with initial data of the form: "smooth deterministic function + a rough random perturbation", as a corollary to Cameron-Martin Theorem and known almost sure global existence results with respect to Gaussian measures on spaces of functions.
Original languageEnglish
Pages (from-to)483-501
Number of pages19
JournalProceedings of the Edinburgh Mathematical Society
Issue number02
Early online date17 Dec 2015
Publication statusPublished - May 2016


  • Gibbs measures
  • white noise
  • invariant measures
  • Cameron-Martin theorem
  • almost sure global existence


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