Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 5 (2011), 1374-1393.
On the discrete approximation of occupation time of diffusion processes
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.
Electron. J. Statist., Volume 5 (2011), 1374-1393.
First available in Project Euclid: 19 October 2011
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Ngo, Hoang-Long; Ogawa, Shigeyoshi. On the discrete approximation of occupation time of diffusion processes. Electron. J. Statist. 5 (2011), 1374--1393. doi:10.1214/11-EJS645. https://projecteuclid.org/euclid.ejs/1319028572