马尔可夫过程H-值可加泛函的向前向后鞅分解(英文)

FORWARD-BACKWARD MARTINGALE DECOMPOSITION FOR H-VALUED ADDITIVE FUNCTIONALS ASSOCIATED WITH MARKOV PROCESSES

本文研究了马尔可夫H-值可加泛函的向前向后鞅分解.利用Lyons-Meyer-Zheng鞅分解得到了泛函数极限定理所必需的极大不等式和紧性结果,在最小条件限度内得到了马尔可夫过程经验测度的泛函中心极限定理,将该定理从实值情形推广到了希尔伯特值情形.

In this paper the forward-backward martingale decomposition is studied. The ingenious forward-backward martingale decomposition of Lyons-Meyer-Zheng is extended to the Hilbert space valued additive functional. This extension gives very directly a maximal inequality and a strong a. s. compactness result required for the functional limit theory. The functional central limit theorem for empirical measures of a Markov process under the minimal condition is extended from real valued case to Hilbert space valued case.