Itô-Krylov's formula for a flow of measures

Thomas Cavallazzi (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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 $.

Mots clés: Itô’s formula; flow of probability measures; linear functional derivative; Krylov’s estimate.

Domaines: Probabilités [math.PR]

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