On Cameron-Martin Theorem and almost sure global existence

2014/05/28 by Tadahiro Oh, Jeremy Quastel, Oh, Tadahiro +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1405.7323

21 pages. Minor modifications. To appear in Proc. Edinb. Math. Soc

arxiv created 2015/07/06 · arxiv updated 2015/07/07

Abstract

In 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.

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