Mathematical Finance and Stochastic Seminar by Wilhelm Stannat: The Lions Derivative in Infinite Dimensions
Speaker: , professor of mathematics, Technische Universität Berlin, Germany
Title: The Lions Derivative in Infinite Dimensions
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 present a mild Ito-formula for Mean-Field SPDEs, which provides the
basis for a higher order Taylor expansion and higher order numerical
schemes.
The talk is based on joint work with J. Spille and A. Vogler.
References
[1] J. Spille, W. Stannat, Pontryagin Maximum Principle for McKean-Vlasov
Reaction-Diffusion Systems, arXiv:2507.16288
[2] W. Stannat, A. Vogler, The Lions Derivative in Infinite Dimensions --
Application to Higher Order Expansion of Mean-Field SPDEs,
arXiv:2407.14884
Stochastic Analysis Seminar