Existence of densities for stable-like driven SDE's with Holder continuous coefficients

被引：37

作者：

Debussche, Arnaud ^{[1
,2
]}

Fournier, Nicolas ^{[3
]}

机构：

[1] IRMAR, F-35170 Bruz, France

[2] ENS Cachan Bretagne, F-35170 Bruz, France

[3] Univ Paris Est, LAMA UMR 8050, Fac Sci & Technol, F-94010 Creteil, France

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2013年 / 264卷 / 08期

关键词：

Levy processes; Stable processes; Stochastic differential equations with jumps; Absolute continuity; Besov spaces;

D O I：

10.1016/j.jfa.2013.01.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Consider a multidimensional stochastic differential equation driven by a stable-like Levy process. We prove that the law of the solution immediately has a density in some Besov space, under some non-degeneracy condition on the driving Levy process and some very light Holder-continuity assumptions on the drift and diffusion coefficients. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：1757 / 1778

页数：22

共 15 条

[1] [Anonymous], 1999, CAMBRIDGE STUD ADV M
[2] [Anonymous], 1992, MONOGR MATH
[3] Integration by parts formula and applications to equations with jumps
Bally, Vlad
Clement, Emmanuelle
[J]. PROBABILITY THEORY AND RELATED FIELDS, 2011, 151 (3-4) : 613 - 657
[4] Holder continuity of solutions of second-order non-linear elliptic integro-differential equations
Barles, Guy
Chasseigne, Emmanuel
Imbert, Cyril
[J]. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2011, 13 (01) : 1 - 26
[5] BICHTELER K, 1983, LECT NOTES MATH, V986, P132
[6] Bichteler K., 1987, STOCHASTICS MONOGR, V2
[7] Debussche A., PROBAB THEO IN PRESS
[8] A criterion of density for solutions of Poisson-driven SDEs
Denis, L
[J]. PROBABILITY THEORY AND RELATED FIELDS, 2000, 118 (03) : 406 - 426
[9] Fournier N., ARXIV12030130
[10] Absolute continuity for some one-dimensional processes
Fournier, Nicolas
Printems, Jacques
[J]. BERNOULLI, 2010, 16 (02) : 343 - 360

← 1 2 →