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The Lions Derivative in Infinite Dimensions and applications to Mean-Field SPDEs

Date(s)
Thursday 27th March 2025 (14:00-15:00)
Contact
Event Convenor Contact: William.Salkeld@nottingham.ac.uk
Description
Speaker's Name: Alexander Vogler
Speaker's Affiliation: TU Berlin
Speaker's Research Theme(s): Statistics and Probability,
Abstract:
We present a new interpretation of the Lions derivative as the Radon-Nikodym derivative of a vector measure, which provides a canonical extension of the Lions derivative for functions taking values in infinite dimensional Banach spaces. This is of particular relevance for the analysis of Hilbert space valued Mean-Field equations. As an application we derive a stochastic maximum principle for controlled Mean-Field stochastic partial differential equations (SPDEs). Furthermore we present a mild Ito-formula for Mean-Field SPDEs, which provides the basis for a higher order Taylor expansion and higher order numerical schemes.

Venue: Physics C5

School of Mathematical Sciences

The University of Nottingham
University Park
Nottingham, NG7 2RD

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