Exponential Convergence in Probability for Empirical Means of Lévy Processes

作     者：Shu-lan Hu Nian Yao 

作者机构：Department of Statistics Zhongnan University of Economics and Law Wuhan 430073 China Department of Mathematics and Statistics Wuhan University Wuhan 430072 China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2010年第26卷第3期

页      面：481-488页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 080503[工学-材料加工工程] 07[理学] 08[工学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0714[理学-统计学（可授理学、经济学学位）] 0802[工学-机械工程] 070103[理学-概率论与数理统计] 0701[理学-数学] 080201[工学-机械制造及其自动化] 

主　　题：L6vy processes exponential convergence in probability large deviations,functions with uniform mean 

摘      要：Let （Xt）t≥0 be a Lévy process taking values in R^d with absolutely continuous marginal distributions. Given a real measurable function f on R^d in Kato＇s class, we show that the empirical mean 1/t ∫ f（Xs）ds converges to a constant z in probability with an exponential rate if and only if f has a uniform mean z. This result improves a classical result of Kahane et al. and generalizes a similar result of L. Wu from the Brownian Motion to general Lévy processes.