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 F...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).展开更多
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)。
文摘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).
