论文标题
由纯跳噪声及其应用驱动的SPDE的可及性
Accessibility of SPDEs driven by pure jump noise and its applications
论文作者
论文摘要
在本文中，我们开发了一种新方法，以获得由加性纯跳噪声驱动的随机部分微分方程的可访问性。本文的重要新颖性是允许驾驶噪声退化。 As an application, for the first time, we obtain the accessibility of a class of stochastic equations driven by pure jump degenerate noise, which cover 2D stochastic Navier-Stokes equations, stochastic Burgers type equations, singular stochastic p-Laplace equations, stochastic fast diffusion equations, etc. As a further application, we establish the ergodicity of singular stochastic p-Laplace equations and stochastic fast diffusion equations在加性纯跳噪声的驱动下，我们指出的是，驾驶噪声可能是带有沉重的尾巴的征费过程。
In this paper, we develop a new method to obtain the accessibility of stochastic partial differential equations driven by additive pure jump noise. An important novelty of this paper is to allow the driving noises to be degenerate. As an application, for the first time, we obtain the accessibility of a class of stochastic equations driven by pure jump degenerate noise, which cover 2D stochastic Navier-Stokes equations, stochastic Burgers type equations, singular stochastic p-Laplace equations, stochastic fast diffusion equations, etc. As a further application, we establish the ergodicity of singular stochastic p-Laplace equations and stochastic fast diffusion equations driven by additive pure jump noise, and we remark that the driving noises could be Levy processes with heavy tails.
