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Itô-Krylov's formula for a flow of measures


We prove Itô's formula for the flow of measures associated with an Itô process having a bounded drift and a uniformly elliptic and bounded diffusion matrix, and for functions in an appropriate Sobolev-type space. This formula is the almost analogue, in the measure-dependent case, of the Itô-Krylov formula for functions in a Sobolev space on $\mathbf{R}^+ \times \mathbf{R}^d $.
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Dates and versions

hal-03373177 , version 1 (11-10-2021)
hal-03373177 , version 2 (07-11-2022)



Thomas Cavallazzi. Itô-Krylov's formula for a flow of measures. 2022. ⟨hal-03373177v2⟩
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