| Issue |
ESAIM: PS
Volume 28, 2024
|
|
|---|---|---|
| Page(s) | 161 - 194 | |
| DOI | https://doi.org/10.1051/ps/2024003 | |
| Published online | 07 May 2024 | |
Itô-Krylov’s Formula for a Flow of Measures
Université Paris-Saclay, CentraleSupélec, MICS and CNRS FR-3487, Gif-sur-Yvette, France
* Corresponding author: thomas.cavallazzi@centralesupelec.fr
Received:
7
November
2022
Accepted:
22
February
2024
In this article, 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 R+ × Rd.
Mathematics Subject Classification: 60H05 / 60H50
Key words: Itô’s formula / flow of probability measures / linear functional derivative / Krylov’s estimate
© The authors. Published by EDP Sciences, SMAI 2024
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