Asymptotic Normality for Singularly Perturbed Diffusion Processes
Date Issued
2010
Date
2010
Author(s)
Chen, Wei-Da
Abstract
Let Xε (·) be a diffusion process satisfying. This diffusion process has two time scales. One is a rapidly changing scale, and the other is a slowly varying scale. In this paper, we are interested in a function of the occupation time of when ε → 0. In our intuition, we think this diffusion will be driven by its fast part when ε → 0. To make our intuition more precisely, we use the asymptoticity for the density of this diffusion to estimate its behavior when ε →0. By virtue of asymptoticity for the density of this diffusion, we will show the law of large
numbers and the asymptotic normality of a function of the occupation time of this process.
Subjects
Singularly perturbed diffusion processes
Type
thesis
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