Martingale approximations for continuous-time and discrete-time stationary Markov processes
Martingale approximations for continuous-time and discrete-time stationary Markov processes
复制标题
连续时间和离散时间平稳马尔可夫过程的鞅近似
DOI：
10.1016/j.spa.2005.04.001
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发表时间：
2005
影响因子：
1.4
通讯作者：
H. Holzmann
中科院分区：
文献类型：
--
作者：
H. Holzmann
本文证明了Kipnis和Varadhan [Comm. Math.Phys.104（1986）1-19]通过预解式构造平稳遍历Markov过程的可加泛函的鞅逼近的方法是普适的，即鞅逼近存在当且仅当预解式表示收敛。给出了鞅逼近存在的一个充分条件。作为例子，我们讨论了移动平均过程和具有正常生成元的过程。
We show that the method of Kipnis and Varadhan [Comm. Math. Phys. 104 (1986) 1–19] to construct a Martingale approximation to an additive functional of a stationary ergodic Markov process via the resolvent is universal in the sense that a martingale approximation exists if and only if the resolvent representation converges. A sufficient condition for the existence of a martingale approximation is also given. As examples we discuss moving average processes and processes with normal generator.