论文标题
单调SPDE的渐近对数 - 摩nack不平等
Asymptotic Log-Harnack Inequality for Monotone SPDE with Multiplicative Noise
论文作者
论文摘要
我们为非线性单调SPDE得出了渐近对数 - 式 - 式摩擦式不等式，这可能是由退化的乘法噪声驱动的。我们的主要工具是渐近耦合度量的变化。作为一种应用，我们表明，在系数上的某些单调和强制性条件下，相应的马尔可夫半群是渐近的砍伐者，渐近的不可约性，并且具有独特的，因此具有独特的且因此不变的度量。结果应用于高度退化的有限二二维或无限差扩散过程。
We derive an asymptotic log-Harnack inequality for nonlinear monotone SPDE driven by possibly degenerate multiplicative noise. Our main tool is the asymptotic coupling by the change of measure. As an application, we show that, under certain monotone and coercive conditions on the coefficients, the corresponding Markov semigroup is asymptotically strong Feller, asymptotic irreducibility, and possesses a unique and thus ergodic invariant measure. The results are applied to highly degenerate finite-dimensional or infinite-dimensional diffusion processes.
