Exponential convergence in probability for empirical means of Lévy processes |
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基金项目: | The authors would like to thank our supervisor, Professor Liming Wu, for his detailed guidance and instructive suggestions. |
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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.
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关 键 词: | 成形过程 概率收敛 指数收敛 边缘分布 绝对连续 可测函数 布朗运动 平均 |
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