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- W3122451100 abstract "We focus on studying the convergence of the martingale solution to two-time-scale SDEs subject to Levy noise. There exist two difficulties. Due to the coupling, the key point in the proof of the convergence is to guarantee the exponential ergodicity of the fast component. Besides, choice of the appropriate pertured test functions plays an decisive role in the martingale methods. The pertured test functions are related to the averaged components in our work. To overcome these difficulties, we go the following steps. Firstly, we investigate SDEs driven by Levy noise without memory, and prove the existence and uniqueness of the solution to the systems. Subsequently, the exponential ergodicity of the ``fast component is exhibited by the several importent inequalities. Convergence of the martingale solution is studied by using martingale methods, based on the exponential ergodicity of the ``fast component and tightness obtaining by virtue of the Arzela-Ascoli theorem. Finally we extend some acquired results for a ``fast component with memory." @default.
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- W3122451100 date "2018-07-18" @default.
- W3122451100 modified "2023-09-23" @default.
- W3122451100 title "Convergence of the martingale solution to two-time-scale SDEs driven by L'evy noise" @default.
- W3122451100 hasPublicationYear "2018" @default.
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