Abstract The asymptotic log-Harnack inequality is established for SPDE with degenerate multiplicative noise by the coupling method. As applications, the gradient estimate, asymptotic strong Feller property, irreducibility, heat kernel estimate and ergodicity are derived.

中文翻译：

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具有退化乘法噪声的 SPDE 的渐近 log-Harnack 不等式及其应用

摘要 采用耦合方法建立了具有退化乘性噪声的SPDE的渐近log-Harnack不等式。作为应用，推导出梯度估计、渐近强Feller性质、不可约性、热核估计和遍历性。