首页|Explicit results for ergodic properties of SDEs driven by cylindrical symmetric stable noises
Explicit results for ergodic properties of SDEs driven by cylindrical symmetric stable noises
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We consider the exponentially ergodic properties of systems of SDEs in Rn driven 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).
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