McKean SDEs with singular coefficients

Elena Issoglio and Francesco Russo

septembre, 2023

Publication type:

Paper in peer-reviewed journals

Journal:

Annales de l'Institut Henri Poincaré. Probabilités et Statistiques., vol. 59 (3), pp. 1530–1548

DOI:

10.1214/22-AIHP1293

HAL:

hal-03306570

arXiv:

2107.14453

Keywords :

Stochastic differential equations; distributional drift; McKean; Martingale problem.

Abstract:

The paper investigates existence and uniqueness for a stochastic differential equation (SDE) with distributional drift depending on the law density of the solution. Those equations are known as McKean SDEs. The McKean SDE is interpreted in the sense of a suitable singular martingale problem. A key tool used in the investigation is the study of the corresponding Fokker-Planck equation.

BibTeX:

@article{Iss-Rus-2023,
    author={Elena Issoglio and Francesco Russo },
    title={McKean SDEs with singular coefficients },
    doi={10.1214/22-AIHP1293 },
    journal={Annales de l'Institut Henri Poincaré. Probabilités et 
           Statistiques. },
    year={2023 },
    month={9},
    volume={59 (3) },
    pages={1530–1548},
}