Functional inequalities for time-changed symmetric α-stable processes

被引：1

作者：

Wang, Jian ^{[1
,2
,3
]}

Zhang, Longteng ^{[4
,5
]}

机构：

[1] Fujian Normal Univ, Coll Math & Informat, Fuzhou 350007, Peoples R China

[2] Fujian Normal Univ, Fujian Key Lab Math Anal & Applicat FJKLMAA, Fuzhou 350007, Peoples R China

[3] Fujian Normal Univ, Ctr Appl Math Fujian Prov FJNU, Fuzhou 350007, Peoples R China

[4] Fujian Normal Univ, Concord Univ Coll, Fuzhou 350007, Peoples R China

[5] Fujian Normal Univ, Coll Math & Informat, Fuzhou 350007, Peoples R China

来源：

FRONTIERS OF MATHEMATICS IN CHINA | 2021年 / 16卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Symmetric α -stable process; time change; functional inequality;

D O I：

10.1007/s11464-021-0908-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish sharp functional inequalities for time-changed symmetric alpha-stable processes on Double-struck capital R-d with d > 1 and alpha is an element of (0, 2), which yield explicit criteria for the compactness of the associated semigroups. Furthermore, when the time change is defined via the special function W(x) = (1 + divide x divide )(beta) with beta > alpha, we obtain optimal Nash-type inequalities, which in turn give us optimal upper bounds for the density function of the associated semigroups.

引用

页码：595 / 622

页数：28

共 50 条

[41] Schramm–Loewner Equations Driven by Symmetric Stable Processes
Zhen-Qing Chen
Steffen Rohde
Communications in Mathematical Physics, 2009, 285
[42] Reflected Symmetric α-Stable Processes and Regional Fractional Laplacian
Qing-Yang Guan
Zhi-Ming Ma
Probability Theory and Related Fields, 2006, 134 : 649 - 694
[43] On exit time of stable processes
Graczyk, Piotr
Jakubowski, Tomasz
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2012, 122 (01) : 31 - 41
[44] Schramm-Loewner Equations Driven by Symmetric Stable Processes
Chen, Zhen-Qing
Rohde, Steffen
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2009, 285 (03) : 799 - 824
[45] Exit times of symmetric α-stable processes from unbounded convex domains
Mendez-Hernandez, Pedro J.
ELECTRONIC JOURNAL OF PROBABILITY, 2007, 12 : 100 - 121
[46] Null flows, positive flows and the structure of stationary symmetric stable processes
Samorodnitsky, G
ANNALS OF PROBABILITY, 2005, 33 (05) : 1782 - 1803
[47] On one-dimensional stochastic equations driven by symmetric stable processes
Engelbert, HJ
Kurenok, VP
STOCHASTIC PROCESSES AND RELATED TOPICS, 2002, 12 : 81 - 109
[48] Symmetry and functional inequalities for stable Lévy-type operators
Huang, Lu-Jing
Wang, Tao
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2025, 183
[49] Inversion of space and time in stable Levy processes
Fourati, S
PROBABILITY THEORY AND RELATED FIELDS, 2006, 135 (02) : 201 - 215
[50] Variational Formula for Dirichlet Forms and Estimates of Principal Eigenvalues for Symmetric α-stable Processes
Yuichi Shiozawa
Masayoshi Takeda
Potential Analysis, 2005, 23 : 135 - 151

← 1 2 3 4 5 →