Exponential mixing for some SPDEs with L\'evy noise
Exponential mixing for some SPDEs with L\'evy noise
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DOI：
10.1142/s0219493711003425
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发表时间：
2010-10
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影响因子：
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通讯作者：
E. Priola;J. Zabczyk;Lihu Xu
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文献类型：
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作者：
E. Priola;J. Zabczyk;Lihu Xu
我们展示了如何梯度估计的过渡半群可以用来建立指数混合一类马尔可夫过程在无限维。我们专注于半线性系统驱动的圆柱$\alpha$-稳定的噪音，$\alpha \在（0，2）$，介绍了Priola-Zabczyk“结构性质的半线性SPDE驱动的圆柱稳定的过程”（PTRF出现）。首先证明了如果非线性项有界，则系统是遍历的强混合的。然后，我们表明，该系统是指数混合提供的非线性，或其Lipschitz常数，是足够小的。
We show how gradient estimates for transition semigroups can be used to establish exponential mixing for a class of Markov processes in infinite dimensions. We concentrate on semilinear systems driven by cylindrical $\alpha$-stable noises, $\alpha \in (0,2)$, introduced in Priola-Zabczyk "Structural properties of semilinear SPDEs driven by cylindrical stable processes" (PTRF to appear). We first prove that if the nonlinearity is bounded, then the system is ergodic and strong mixing. Then we show that the system is exponentially mixing provided that the nonlinearity, or its Lipschitz constant, are sufficiently small.