Asymptotic Normality for Singularly Perturbed Diffusion Processes

• Main Authors: Wei-Da Chen, 陳韋達
• Other Authors: 姜祖恕
• Format: Others
• Language: zh-TW
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/90151813813773093587

碩士 === 臺灣大學 === 數學研究所 === 98 === 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.