Wednesday, May 21, 2025 - 09:30 in V2-210
Existence of moments for the (linear) Parabolic Anderson model with singular fractional noise
A talk in the SPDEvent series by
Sophie Mildenberger from Universität Münster
| Abstract: |
In this talk, we are concerned with the existence of moments for solutions of the (linear) Parabolic Anderson model for a class of fractional space-time white noises with parabolic regularity in $(-4/3,-1]$. Working within the framework of Regularity Structures, we establish pathwise interior estimates on time intervals with a small model norm. Iterative application of these estimates along a partition of time leads to moment bounds in terms of a stochastic quantity related to the model. We use the Gaussian isoperimetric inequality to prove suitable tail estimates for this quantity. The argument heavily relies on analytic homogeneity bounds on recentered Young products of distributions in mixed Besov scales of dominating mixed smoothness.
|
Back
