带乘性Poisson噪声的非线性随机发展方程的遍历性
Ergodicity for nonlinear stochastic evolution equations with multiplicative Poisson noise
摘要：
研究了变分情形下带单调漂移和乘性Poisson噪声的随机发展方程解的渐近性态，从而涵盖了一大类带跳跃噪声扰动的（完全）非线性偏微分方程.特别地，我们提供了不变测度的存在性、遍历性和唯一性的充分条件。进一步，在适当的附加假设下，我们证明了与带加性噪声的随机方程相关联的Kolmogorov方程在$L_1$空间中关于一个不变测度是可解的.
英文摘要：
We study the asymptotic behavior of solutions to stochastic evolution equations with monotone drift and multiplicative Poisson noise in the variational setting, thus covering a large class of (fully) nonlinear partial differential equations perturbed by jump noise. In particular, we provide sufficient conditions for the existence, ergodicity, and uniqueness of invariant measures. Furthermore, under mild additional assumptions, we prove that the Kolmogorov equation associated to the stochastic equation with additive noise is solvable in $L_1$ spaces with respect to an invariant measure.
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