English

It{\^o}-Krylov's formula for a flow of measures

Probability 2022-11-09 v2

Abstract

We prove It{\^o}'s formula for the flow of measures associated with an It{\^o} 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 It{\^o}-Krylov formula for functions in a Sobolev space on R+×Rd\mathbf{R}^+ \times \mathbf{R}^d .

Keywords

Cite

@article{arxiv.2110.05251,
  title  = {It{\^o}-Krylov's formula for a flow of measures},
  author = {Thomas Cavallazzi},
  journal= {arXiv preprint arXiv:2110.05251},
  year   = {2022}
}