Itô-Wentzell-Lions Formula for Measure Dependent Random Fields under Full and Conditional Measure Flows

We present several Itô-Wentzell formulae on Wiener spaces for real-valued functional random field of Itô type that depend on measure flows. We distinguish the full- and the marginal-measure flow cases in the spirit of mean-field games. Derivatives with respect to the measure components are understoo...

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Veröffentlicht in:	Potential analysis 2023-10, Vol.59 (3), p.1313-1344
Hauptverfasser:	dos Reis, Gonçalo, Platonov, Vadim
Format:	Artikel
Sprache:	eng
Schlagworte:	Fields (mathematics) Functional Analysis Geometry Mathematics Mathematics and Statistics Potential Theory Probability Theory and Stochastic Processes
Online-Zugang:	Volltext
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