论文标题
BROX扩散的无限发电机
The infinitesimal generator of the Brox diffusion
论文作者
论文摘要
我们在具有周期性布朗环境的线上构建了Brox扩散的无限发电机。这为过程提供了新的结构，并允许解决单一的群众问题。我们证明，相关的半群是强劲的砍伐者，高斯下层和上限。这还产生了具有周期性或迪基莱特边界条件的细分市场上BROX扩散的构造。在这个有界的空间中，我们证明存在一个独特的度量，并且存在光谱差距，从而给出了扩散的指数性成分。
We construct the infinitesimal generator of the Brox diffusion on a line with a periodic Brownian environment. This gives a new construction of the process and allows to solve the singular martingale problem. We prove that the associated semigroup is strong Feller with Gaussian lower and upper bounds. This also yields a construction of the Brox diffusion on a segment with periodic or Dirichlet boundary conditions. In this bounded space, we prove that there exists a unique measure and the existence of a spectral gap giving exponential ergodicity of the diffusion.
