Wednesday, October 26, 2022 - 14:00 in V3-201 + Zoom
Path-wise central limit theorem and moderate deviations via rough paths for a class of SPDEs with multiplicative small noise.
A talk in the Bielefeld Stochastic Afternoon series by
Emanuela Gussetti
| Abstract: |
We employ the theory of rough paths to establish a path-wise central limit theorem (CLT) and a moderate deviation principle (MDP) for the deviations of a class of SDEs and SPDEs perturbed with a small multiplicative noise from the deterministic solution. The CLT can be interpreted as a path-wise derivative of the It\^o-Lyons map. The result follows from the application of a path-wise Malliavin-like calculus for rough paths and compactness methods. From the exponential equivalence principle, we can derive easily a MDP. In particular, we do not apply the weak convergence approach usually employed in this framework. As an application, we derive a path-wise central limit theorem and a moderate deviation principle for the stochastic Landau-Lifschitz-Gilbert equation in 1D. We derive also path-wise convergence to the CLT limit for equations driven by linear It\^o noise and a corresponding MDP. We discuss some applications to non-linear filtering problems.
Within the CRC this talk is associated to the project(s): B7 |
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