Monday, July 10, 2023 - 09:30 in ZiF
Linear SPDEs driven by Lévy generators: optimal regularity of the solution
A talk in the SPDEs, optimal control and mean field games series by
Marta Sanz-Solé from Barcelona
| Abstract: |
We consider parabolic and hyperbolic SPDEs on $(0, \infty)\times\mathbb{R}^d$ of the form $\delta_t u = Lu+g(u)+ \dot W$ and $\delta_t^2 u = Lu+c+\dot W$, with suitable initial data, forced with a space-time
homogeneous Gaussian noise
$\dot W$ that is white in its time variable and correlated
in its space variable, and where L is the generator of a non-degenerate d-dimensional
Lévy process X. We will exhibit optimal Hölder continuous conditions for the
respective random-field solutions to these SPDEs. These conditions are stated
in terms of indices that describe thresholds on the integrability of some functionals
of the characteristic exponent of the process X with respect to the spectral
measure of the spatial covariance of W . This talk is based on joint work with
Davar Khosnevishan.
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