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Proceedings of the Edinburgh Mathematical Society (1)

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On the Cameron–Martin theorem and almost-sure global existence
Tadahiro Oh, Jeremy Quastel
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 59 / Issue 2 / May 2016

Published online by Cambridge University Press:

17 December 2015, pp. 483-501
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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.