The Lions Derivative in Infinite Dimensions and Higher Order Expansion of Mean-Field SPDEs
Abstract
In this paper 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 illustration we derive a mild Ito-formula for Mean-Field stochastic partial differential equations (SPDEs), which provides the basis for a higher order Taylor expansion and higher order numerical schemes.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.14884
- arXiv:
- arXiv:2407.14884
- Bibcode:
- 2024arXiv240714884V
- Keywords:
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- Mathematics - Probability