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

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
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Zusammenfassung: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 understood in the sense of Lions.
ISSN:0926-2601
1572-929X
DOI:10.1007/s11118-022-10012-1