Local densities for a class of degenerate diffusions

被引：4

作者：

Lanconelli, Alberto ^{[1
]}

Pagliarani, Stefano ^{[2
]}

Pascucci, Andrea ^{[3
]}

机构：

[1] Univ Bari Aldo Moro, Dipartimento Matemat, Bari, Italy

[2] Univ Udine, DIES, Udine, Italy

[3] Univ Bologna, Dipartimento Matemat, Bologna, Italy

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2020年 / 56卷 / 02期

关键词：

Hormander condition; Intrinsic geometry; Intrinsic Holder spaces; Kolmogorov equations; Local densities; Strong Feller property; TAYLOR FORMULA;

D O I：

10.1214/19-AIHP1009

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study a class of R-d-valued continuous strong Markov processes that are generated, only locally, by an ultra-parabolic operator with coefficients that are regular w.r.t. the intrinsic geometry induced by the operator itself and not w.r.t. the Euclidean one. The first main result is a local Ito formula for functions that are not twice-differentiable in the classical sense, but only intrinsically w.r.t. to a set of vector fields, related to the generator, satisfying the Hormander condition. The second main contribution, which builds upon the first one, is an existence and regularity result for the local transition density.

引用

页码：1440 / 1464

页数：25