Heat kernel and gradient estimates for kinetic SDEs with low regularity coefficients

P E Chaudru de Raynal (1) , S Menozzi (2, 3) , A Pesce (4) , X Zhang (5)

1 Département de Mathématiques et Informatique - Université de Nantes
2 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry
3 HSE - Vysšaja škola èkonomiki = National Research University Higher School of Economics [Moscow]
4 UNIBO - Alma Mater Studiorum Università di Bologna = University of Bologna
5 Wuhan University [China]

We establish heat kernel and gradient estimates for the density of kinetic degenerate Kolmogorov stochastic differentia equations. Our results are established under somehow minimal assumptions that guarantee the SDE is weakly well posed.

Mots clés: degenerate Kolmogorov kinetic equations; heat kernel and gradient estimates; parametrix; parametrix MSC: 60H10; 34F05; degenerate Kolmogorov equations; kinetic dynamics

Domaines: Probabilités [math.PR]; Equations aux dérivées partielles [math.AP]

P E Chaudru de Raynal, S Menozzi, A Pesce, X Zhang. Heat kernel and gradient estimates for kinetic SDEs with low regularity coefficients. 2022. ⟨hal-03553730v1⟩