Explicit results for ergodic properties of SDEs driven by cylindrical symmetric stable noises  

作　　者：Lu-Jing Huang Jian Wang 

机构地区：[1]School of Mathematics and Statistics,Fujian Normal University,Fuzhou,350007,China [2]Key Laboratory of Analytical Mathematics and Applications(Ministry of Education),Fujian Normal University,Fuzhou,350007,China [3]Fujian Key Laboratory of Analytical Mathematics and Applications,Fujian Normal University,Fuzhou,350007,China [4]Center for Applied Mathematics of Fujian Province,Fujian Normal University,Fuzhou,350007,China

出　　处：《Science China Mathematics》2024年第12期2823-2842,共20页中国科学（数学英文版）

基　　金：supported by the National Key R&D Program of China(Grant No.2022YFA1006003);National Natural Science Foundation of China(Grant Nos.11831014,12071076,and 12225104)。

摘　　要：We consider the exponentially ergodic properties of systems of SDEs in Rndriven by cylindrical stable processes,potentially with different indices across different coordinates.Our approach is based on the well-known Foster-Lyapunov criteria and a careful selection of Lyapunov functions,alongside recent advances in regularity and transition density estimates for solutions to SDEs driven by Lévy processes with independent coordinates.These results are novel,even in the one-dimensional case.Notably,our findings suggest that multiplicative cylindrical stable processes can enhance the ergodicity of the system when the stable noise indices in all directions fall within[1,2).

关 键 词：cylindrical stable process exponential ergodicity strong ergodicity Foster-Lyapunov criterion strong Feller property 

分 类 号：O177.99[理学—数学]