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2011 On the discrete approximation of occupation time of diffusion processes
Hoang-Long Ngo, Shigeyoshi Ogawa
Electron. J. Statist. 5: 1374-1393 (2011). DOI: 10.1214/11-EJS645

Abstract

Let X be a 1-dimensional diffusion process. We study a simple class of estimators, which rely only on one sample data $\{X_{\frac{i}{n}},0\leq i\leq nt\}$, 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 n3/4. 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 n1/2. Some discussions about the exactness of the rates are also presented.

Citation

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Hoang-Long Ngo. Shigeyoshi Ogawa. "On the discrete approximation of occupation time of diffusion processes." Electron. J. Statist. 5 1374 - 1393, 2011. https://doi.org/10.1214/11-EJS645

Information

Published: 2011
First available in Project Euclid: 19 October 2011

zbMATH: 1271.60086
MathSciNet: MR2842909
Digital Object Identifier: 10.1214/11-EJS645

Subjects:
Primary: 60F55, 60J60
Secondary: 60J55

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

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