On the Cameron-Martin theorem and almost-sure global existence (Q2806130)
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scientific article; zbMATH DE number 6580775
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Cameron-Martin theorem and almost-sure global existence |
scientific article; zbMATH DE number 6580775 |
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13 May 2016
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Cameron-Martin theorem
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almost-sure global existence
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nonlinear Hamiltonian partial differential equation
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rough random perturbation
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Gibbs measure
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white noise
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On the Cameron-Martin theorem and almost-sure global existence (English)
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The authors consider almost-sure global existence results for some nonlinear Hamiltonian partial differential equations (PDEs). The results are corollaries to the classical Cameron-Martin theorem and to known almost-sure global existence results with respect to Gaussian measures on spaces of functions. In particular, almost-sure global existence is established for initial data having the form of the sum of a smooth deterministic function and a rough random perturbation, white noise being one of its examples. Invariant Gibbs measures for Hamiltonian PDEs are discussed and their variational characterization is presented.
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