On the Cameron–Martin theorem and almost-sure global existence

Abstract

AbstractIn this paper we discuss various aspects of invariant measures for nonlinear Hamiltonian partial differential equations (PDEs). In particular, we show almost-sure global existence for some Hamiltonian PDEs with initial data of the form ‘a smooth deterministic function + a rough random perturbation’ as a corollary to the Cameron–Martin theorem and known almost-sure global existence results with respect to Gaussian measures on spaces of functions.