The objective of this course is to introduce basic concepts for stochastic processes. The main focus will be on studying analytical models for systems which change states stochastically with time. The topics include:
1. Markov Chains
1A. Hidden Markov Models
2. Poisson processes
2A. Non-homogeneous Poisson processes
3. Continuous-Time Markov Chain
3A. Queueing Models
4. Renewal Theorem
4A. Apply Renewal Theorem to Reliability
5. Brownian motion and MArtingales
5A. Black-Scholes Models and Related Topics
The objective of this course is to introduce basic concepts for stochastic processes. The main focus will be on studying analytical models for systems which change states stochastically with time. The topics include:
1.Markov Chains
1A. Hidden Markov Models
2.Poisson processes
2A. Non-homogeneous Poisson processes
3. Continuous-Time Markov Chain
3A.Queueing Models
4. Renewal Theorem
4A. Apply Renewal Theorem to Reliability
5.Brownian motion and MArtingales
5A. Black-Scholes Models and Related Topics
The objective of this course is to introduce basic concepts for stochastic processes. The main focus will be on studying analytical models for systems which change states stochastically with time. This is a course for studying probabilistic models rather than statistical models. Thus, background on probability and mathematical statistics are necessary. We will begin right after �onditional probability�and �onditional expectation� Students will learn concepts and techniques for characterizing models stochastically. This will help students for further study. The topics of this course include basic processes, stochastic models, and diffusion processes. Contents of this course might be adjusted according to time limitation and students�interests. They are:
1.Preliminaries: lack of memory property, transformations, inequalities, limit theorems, notations of stochastic processes
2.Markov chains: Chapman-Kolmogorov equation, classification of chains, long run behavior of Markov chains, branch processes, random walk
3.Poisson processes: Inter-arrival time distributions, conditional waiting time distributions, non-homogeneous Poisson processes
4.Continuous-time Markov chains: birth-death processes, compound Poisson processes, finite-state Markov chains
5.Renewal processes: renewal functions, limit theorems, delayed and stationary renewal processes, queueing
6.Stochastic models: Markov renewal processes, marked processes
7.Martingales: conditional expectations, filtrations, stopping time, martingale CLT
8.Diffusion Processes: Brownian motions, It�s formula, Black-Scholes Model, Girsanov Theorem
The objective of this course is to introduce basic concepts for stochastic processes. The main focus will be on studying analytical models for systems which change states stochastically with time. This is a course for studying probabilistic models rather than statistical models. Thus, background on probability and mathematical statistics are necessary. We will begin right after �onditional probability�and �onditional expectation� Students will learn concepts and techniques for characterizing models stochastically. This will help students for further study. The topics of this course include basic processes, stochastic models , and diffusion processes. Contents of this course might be adjusted according to time limitation and students’ interests. They are:
1.Preliminaries: lack of memory property, transformations, inequalities, limit theorems, notations of stochastic processes
2.Markov chains: Chapman-Kolmogorov equation, classification of chains, long run behavior of Markov chains, branch processes, random walk
3.Poisson processes: Inter-arrival time distributions, conditional waiting time distributions, non-homogeneous Poisson processes
4.Continuous-time Markov chains: birth-death processes, compound Poisson processes, finite-state Markov chains
5.Renewal processes: renewal functions, limit theorems, delayed and stationary renewal processes, queuing
6.Stochastic models: Markov renewal processes, marked processes
7.Martinales: conditional expectations, filtrations, stopping time, martingale CLT
8.Diffusion Processes: Brownian motions, Its formula, Black-Scholes Model, Girsanov Theorem
1. Sheldon M. Ross (2014) Introduction to Probability Models, 11th ed, Academic Press
2. Sheldon M. Ross (1996) Stochastic Processes, 2nd ed, John Wiley , New York.
1. Sheldon M. Ross (2014) Introduction to Probability Models, 11th ed, Academic Press
2. Sheldon M. Ross (1996) Stochastic Processes, 2nd ed, John Wiley, New York.
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| AssignmentsAssignments assignments |
30 | 2-3 assignments |
| Mid-term ExamMid-term Exam mid-term exam |
30 | |
| Project ReportProject Report project report |
40 |
