111年第1學期-6191 隨機過程專題（一） 課程資訊

評分方式

評分項目	配分比例	說明
Report - 1	50
Report - 2	50

教育目標

This course will study some specific point processes and continuous-time dynamic system. The main focus will be on the Hawkes Process and Kalman-Bucy Filter.

課程概述

Stochastic processes based methods are often used in dynamic data analysis. In this course, we focus on diffusion models which can be expressed by a time-dependent drift coefficient, a diffusion coefficient, and a Brownian motion. To characterize the dynamic behavior of the diffusion process, we focus on the drift coefficient for two different approaches. One approach relates to the Hawkes process, and the other approach involves the Kalman-Bucy filter. Applications include financial derivatives pricing and system reliability analysis.

基本資料

選修課，學分數：3-0
上課時間：二/7,8,9[M438]
修課班級：統計博6
修課年級：年級以上
選課備註：

參考書目

1. S. I. Resnick (1992) Adventures in Stochastic Processes, Birkhauser.
2. D.J. Daley, D. Vere-Jones (2003) An introduction to the theory of point processes: Volume I: Elementary Theory and Methods.
3. S.N. Neftci (2000) An Introduction to the Mathematics of Financial Derivatives (2nd ed) Academic Press.
4. L.C.G. Rogers, D. Williams (2000) Diffusion, Markov Processes, and Martingales, Volumn 2: Ito Calculus (2nd ed) Cambridge University Press.