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Self-normalized Cramér-type Moderate Deviations for Functionals of Markov Chain
Acta Mathematicae Applicatae Sinica, English Series ( IF 0.9 ) Pub Date : 2020-03-01 , DOI: 10.1007/s10255-020-0924-5
Xin-wei Feng , Qi-Man Shao

Let xn, n ≥ 0} be a Markov chain with a countable state space S and let f(·) be a measurable function from S to ℝ and consider the functionals of the Markov chain yn:= f(xn). We construct a new type of self-normalized sums based on the random-block scheme and establish a Cramer-type moderate deviations for self-normalized sums of functionals of the Markov chain.

中文翻译:

马尔可夫链泛函的自归一化克拉默型中等偏差

设 xn, n ≥ 0} 是一个具有可数状态空间 S 的马尔可夫链,让 f(·) 是一个从 S 到 ℝ 的可测函数,并考虑马尔可夫链 yn:= f(xn) 的泛函。我们基于随机块方案构造了一种新型的自归一化和,并为马尔可夫链的泛函的自归一化和建立了克拉默型的适度偏差。
更新日期:2020-03-01
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