论文标题
非对称过程的马尔可夫链近似
Markov chain approximations for nonsymmetric processes
论文作者
论文摘要
本文的目的是证明，在$ n^{ - 1} \ Mathbb {z}^d $上，可以通过合适的Markov链在$ \ mathbb {r}^d $中进行的扩散过程近似。此外，我们研究了足够的电导条件，以确保相关的马尔可夫链与此类马尔可夫过程的收敛。对于大量非对称跳跃过程，回答了类似的问题。我们结果的证明取决于对相应的非对称抛物线方程和Dirichlet形式技术的弱解决方案的规律性估计。
The aim of this article is to prove that diffusion processes in $\mathbb{R}^d$ with a drift can be approximated by suitable Markov chains on $n^{-1}\mathbb{Z}^d$. Moreover, we investigate sufficient conditions on the conductances which guarantee convergence of the associated Markov chains to such Markov processes. Analogous questions are answered for a large class of nonsymmetric jump processes. The proofs of our results rely on regularity estimates for weak solutions to the corresponding nonsymmetric parabolic equations and Dirichlet form techniques.
