# 107年第2學期-6196 隨機過程專題 課程資訊

Homework 50
Report 50

## 教育目標

This course studies some topics of point processes which have been applied substantially in dynamic data analysis recently. In this course, the focus will be on several topics extended and generalized from the Poisson processes. The contents of this course include filtered marked Poisson processes, doubly stochastic Poisson processes, and hidden Markov processes. This course discusses both methodologies and applications. For filtered marked Poisson processes, the theoretical emphases will be on shot noise and Poisson driven Markov processes. For doubly Poisson processes, the emphases will be on filtering problems. For hidden Markov processes, issues will be finite and infinite channels. Financial derivatives and system reliability will serve as the base for applications.

## 課程概述

This course studies some topics of point processes which have been applied substantially in dynamic data analysis recently. In this course, the focus will be on several topics extended and generalized from the Poisson processes. The contents of this course include filtered marked Poisson processes, doubly stochastic Poisson processes, and hidden Markov processes. This course discusses both methodologies and applications. For filtered marked Poisson processes, the theoretical emphases will be on shot noise and Poisson driven Markov processes. For doubly Poisson processes, the emphases will be on filtering problems. For hidden Markov processes, issues will be finite and infinite channels. Financial derivatives and system reliability will serve as the base for applications.

## 參考書目

1. D.R. Cox, V. Isham (1980) Point Processes, Chapman & Hall.
2. S. I. Resnick (1992) Adventures in Stochastic Processes, Birkhauser.
3. D.J. Daley, D. Vere-Jones (2003) An introduction to the theory of point processes: Volume I: Elementary Theory and Methods.
4. R. Bhar, S. Hamori (2004) Hidden Markov Models: Applications to Financial Economics, Kluwer Academic Publishers.
5. T. Mikosch (2004) Non-Life Insurance Mathematics: An Introduction with Stochastic Processes, Springer.
6. V. S. Barbu, N. Limnios (2008) Semi-Markov Chains and Hidden Semi-Markov Models toward Applications: Their Use in Reliability and DNA Analysis, Springer.