文章基本信息

标题：On the discrete approximation of occupation time of diffusion processes
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作者：Hoang-Long Ngo ; Shigeyoshi Ogawa
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2011
卷号：5
页码：1374-1393
DOI：10.1214/11-EJS645
语种：English
出版社：Institute of Mathematical Statistics
摘要：Let X be a 1-dimensional diffusion process. We study a simple class of estimators, which rely only on one sample data , for the occupation time ∫0tIA(Xs)ds of process X in some set A. The main concern of this paper is the rates of convergence of the estimators. First, we consider the case that A is a finite union of some intervals in ℝ, then we show that the estimator converges at rate n−3/4. Second, we consider the so-called stochastic corridor in mathematical finance. More precisely, we let A be a stochastic interval, say [Xt0,∞) for some t0∈(0,t), then we show that the estimator converges at rate n−1/2. Some discussions about the exactness of the rates are also presented.