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.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, double stochastic Poisson processes, and hidden Markov processes. This course discusses both methods and applications. For filtered marked Poisson processes, the theoretical emphasises will be on shot noise and Poisson driven Markov processes. For double Poisson processes, the emphasises 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.
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.
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, double stochastic Poisson processes, and hidden Markov processes. This course discusses both methods and applications. For filtered marked Poisson processes, the theoretical emphasises will be on shot noise and Poisson driven Markov processes. For double Poisson processes, the emphasises 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.
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.
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 towards Applications: Their Use in Reliability and DNA Analysis, Springer.
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| HomeworkHomework Homework |
50 | |
| ReportReport Report |
50 |
