Repository landing page

We are not able to resolve this OAI Identifier to the repository landing page. If you are the repository manager for this record, please head to the Dashboard and adjust the settings.

Fréchet differentiability of mild solutions to SPDEs with respect to the initial datum

Abstract

We establish n-th-order Fréchet differentiability with respect to the initial datum of mild solutions to a class of jump diffusions in Hilbert spaces. In particular, the coefficients are Lipschitz-continuous, but their derivatives of order higher than one can grow polynomially, and the (multiplicative) noise sources are a cylindrical Wiener process and a quasi-left-continuous integer-valued random measure. As preliminary steps, we prove well-posedness in the mild sense for this class of equations, as well as first-order Gâteaux differentiability of their solutions with respect to the initial datum, extending previous results by Marinelli, Prévôt, and Röckner in several ways. The differentiability results obtained here are a fundamental step to construct classical solutions to non-local Kolmogorov equations with sufficiently regular coefficients by probabilistic means

Similar works

Full text

thumbnail-image

Archivio istituzionale della ricerca - Politecnico di Milano

redirect
Last time updated on 15/08/2022

Having an issue?

Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.