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

Published online by Cambridge University Press:  17 December 2015

Tadahiro Oh
Affiliation:
School of Mathematics, University of Edinburgh and The Maxwell Institute for the Mathematical Sciences, James Clerk Maxwell Building, The King’s Buildings, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK ([email protected])
Jeremy Quastel
Affiliation:
Departments of Mathematics and Statistics, University of Toronto, 40 St. George Street, Toronto, Ontario M5S 2E4, Canada ([email protected]) and School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA

Abstract

In 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.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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