论文标题
马尔可夫链近似一维扩散
Markov chain approximations for one dimensional diffusions
论文作者
论文摘要
本文研究了一维对称扩散的马尔可夫链近似。给定在封闭间隔内具有比例函数$ s $和速度度量$ m $的不可约的反射扩散，近似的马尔可夫链是通过与扩散相对应的dirichlet形式的痕迹明确构建的。我们方法的一个特征是，正如以前的相关作品中通常所施加的那样，它在极限对象的扩散系数或近似马尔可夫链的电导的扩散系数上不需要均匀的椭圆率。
The Markov chain approximation of a one-dimensional symmetric diffusion is investigated in this paper. Given an irreducible reflecting diffusion on a closed interval with scale function $s$ and speed measure $m$, the approximating Markov chains are constructed explicitly through the trace of the Dirichlet form corresponding to the diffusion. One feature of our approach is that it does not require uniform ellipticity on diffusion coefficient of the limit object or uniform regularity on conductances of the approximative Markov chains, as imposed usually in the previous related works.
