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- W2976949979 abstract "Dans cet article, nous étudions le comportement du bruit des solutions d’une équation de Langevin non linéaire du second ordre $ddot{x}^{varepsilon}_{t}+|dot{x}^{varepsilon}_{t}|^{beta}=dot{Z}^{varepsilon}_{varepsilon t}$, $betainmathbb{R}$, dirigée par un processus de Lévy $Z^{varepsilon}$ symétrique et non Gaussien. Cette équation décrit la dynamique d’un système mécanique à un degré de liberté soumis à un frottement non linéaire et à des vibrations aléatoires. Pour un bruit de Grenaille (quantique, shot noise), le processus $x^{varepsilon}$ sur l’échelle de temps macroscopique $t/varepsilon$ s’interprète naturellement comme un filtre non linéaire qui réagit à chaque saut du processus $Z$. Nous montrons qu’un système conduit par un bruit de Lévy symétrique présente le même comportement asymptotique sous la condition principale $alpha+2beta<4$, où $alphain[0,2]$ est l’indice Blumenthal–Getoor « uniforme » de la famille ${Z^{varepsilon}}_{varepsilon>0}$." @default.
- W2976949979 created "2019-10-03" @default.
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- W2976949979 date "2019-08-01" @default.
- W2976949979 modified "2023-09-24" @default.
- W2976949979 title "Non-Gaussian limit theorem for non-linear Langevin equations driven by Lévy noise" @default.
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- W2976949979 doi "https://doi.org/10.1214/18-aihp919" @default.
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