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Itô-Wentzell-Lions Formula for Measure Dependent Random Fields under Full and Conditional Measure Flows
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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.
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© 2022, The Author(s).
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Conditional measure flows Full measure flows Itô-Wentzell formula Lions derivative Stochastic differential equations Analysis