English

An analytic approach to infinite-dimensional continuity and Fokker-Planck-Kolmogorov equations

Probability 2018-06-18 v1

Abstract

We prove a new uniqueness result for solutions to Fokker-Planck-Kolmogorov (FPK) equations for probability measures on infinite-dimensional spaces. We consider infinite-dimensional drifts that admit certain finite-dimensional approximations. In contrast to most of the previous work on FPK-equations in infinite dimensions, we include cases with non-constant coefficients in the second order part and also include degenerate cases where these coefficients can even be zero. Also a new existence result is proved. Some applications to Fokker-Planck-Kolmogorov equations associated with SPDEs are presented.

Keywords

Cite

@article{arxiv.1305.7348,
  title  = {An analytic approach to infinite-dimensional continuity and Fokker-Planck-Kolmogorov equations},
  author = {Vladimir I. Bogachev and Giuseppe Da Prato and Michael Röckner and Stanislav V. Shaposhnikov},
  journal= {arXiv preprint arXiv:1305.7348},
  year   = {2018}
}