鞅逼近与预解式表示收敛的几个定理

Theorems about Martingale Approximation and Resolvent Representation Convergence

通过引入平稳遍历Markov过程的鞅逼近和St(f)的预解式表示,给出并证明了St(f)存在鞅逼近当且仅当预解式表示收敛,对于Markov链有相应的公式化结果.表明通过预解式构造平稳遍历Markov过程加性泛函的鞅逼近方法在此意义下具有普遍性.

By means of introduction martingale approximation of stationary ergodic Markov process and the resolvent representation of St（f）, it is improved that a martingale approximation of St（f） exists if and only if the resolvent representation of St（f） converges and corresponding results are also formulated for Markov chains, showing that the method of constructing a martingale approximation to an additive functional of a stationary ergodic Markov process via the resolvent has universality under this kind of condition.