Heat Kernel Estimates for Stable-driven SDEs with Distributional Drift

被引:0
作者
Fitoussi, Mathis [1 ]
机构
[1] Univ Paris Saclay, Univ Evry Val dEssonne, Lab Math & Modelisat Evry LaMME, ENSIIE,UMR CNRS 8071, 23 Blvd France, F-91037 Evry, France
关键词
Heat kernel estimates; Singular drift diffusions; Stable SDEs; STOCHASTIC DIFFERENTIAL-EQUATIONS; UNIQUENESS; CONSTRUCTION; DENSITY;
D O I
10.1007/s11118-023-10115-3
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We consider the formal SDEdX(t)=b(t,X-t)dt+dZ(tt),X0=x is an element of R-d,(E)where b is an element of L (R)([0,T],B-p,q(beta)(R-d,R-d)) is a time-inhomogeneous Besov drift and Z(t )is a symmetric d-dimensional alpha-stable process, alpha is an element of (1,2), whose spectral measure is absolutely continuous w.r.t. the Lebesgue measure on the sphere. Above, Lr and B beta p,q respectively denote Lebesgue and Besov spaces. We show that, when beta>1-alpha+alpha r+d/p/2, the martingale solution associated with the formal generator of (E) admits a density which enjoys two-sided heat kernel bounds as well as gradient estimates w.r.t. the backward variable. Our proof relies on a suitable mollification of the singular drift aimed at using a Duhamel-type expansion. We then use a normalization method combined with Besov space properties (thermic characterization, duality and product rules) to derive estimates.
引用
收藏
页码:431 / 461
页数:31
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