Density and gradient estimates for non degenerate Brownian SDEs with unbounded measurable drift

被引：29

作者：

Menozzi, S. ^{[1
,2
]}

Pesce, A. ^{[3
]}

Zhang, X. ^{[4
]}

机构：

[1] Univ Evry Val dEssonne, Lab Modelisat Math Evry LaMME, 23 Blvd France, F-91037 Evry, France

[2] HSE, Lab Stochast Anal, Pokrovsky Blvd 11, Moscow, Russia

[3] Dipartimento Matemat, Piazza Porta San Donato 5, Bologna, Italy

[4] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2021年 / 272卷

关键词：

Unbounded drift; Heat kernel estimates; Gradient estimates; Parametrix method; FUNDAMENTAL-SOLUTIONS; VARIATIONAL REPRESENTATION; FUNCTIONALS; UNIQUENESS; EQUATIONS; OPERATORS; FORMULA;

D O I：

10.1016/j.jde.2020.09.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider non degenerate Brownian SDEs with Holder continuous in space diffusion coefficient and unbounded drift with linear growth. We derive two sided bounds for the associated density and pointwise controls of its derivatives up to order two under some additional spatial Wilder continuity assumptions on the drift. Importantly, the estimates reflect the transport of the initial condition by the unbounded drift through an auxiliary, possibly regularized, flow. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：330 / 369

页数：40

共 29 条

[1]

[Anonymous], 1979, GRUNDLEHREN MATH WIS

[2]

Aronson D.G., 1959, ILLINOIS J MATH, V3, P580

[3] BOUNDS FOR FUNDAMENTAL SOLUTION OF A PARABOLIC EQUATION [J].

ARONSON, DG .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1967, 73 (06) :890-&

[4]

Bass R.F., 1997, DIFFUSIONS ELLIPTIC

[5]

Bass RF, 2009, ASTERISQUE, P47

[6] Fundamental solutions for non-divergence form operators on stratified groups [J].

Bonfiglioli, A ;

Lanconelli, E ;

Uguzzoni, F .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 356 (07) :2709-2737

[7]

Boué M, 1998, ANN PROBAB, V26, P1641

[8] KERNEL ESTIMATES FOR ELLIPTIC OPERATORS WITH UNBOUNDED DIFFUSION, DRIFT AND POTENTIAL TERMS [J].

Boutiah, Sallah Eddine ;

Rhandi, Abdelaziz ;

Tacelli, Cristian .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2019, 39 (02) :803-817

[9] Heat kernels for non-symmetric diffusion operators with jumps [J].

Chen, Zhen-Qing ;

Hu, Eryan ;

Xie, Longjie ;

Zhang, Xicheng .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 263 (10) :6576-6634

[10] Strong existence and uniqueness for degenerate SDE with Holder drift [J].

de Raynal, P. E. Chaudru .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2017, 53 (01) :259-286

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