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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  and
Jeremy Quastel
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
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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.

Keywords

Gibbs measureswhite noiseinvariant measuresCameron-Martin theoremalmost-sure global existencePrimary 60H4060H3035Q5535Q53
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 2 , May 2016 , pp. 483 - 501
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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