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arXiv · 1405.7323

On Cameron-Martin Theorem and almost sure global existence

Tadahiro Oh·Jeremy Quastel
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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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Tadahiro Oh, Jeremy Quastel. 2014-05-28. On Cameron-Martin Theorem and almost sure global existence. https://arxiv.org/abs/1405.7323

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