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) discrete-time Markov chains (classification of states, periodicity, ergodic, finite-state Markov chain), (1A) hidden Markov models, (2) Poisson process (definitions and properties), (2A) non-homogeneous Poisson processes (properties and applications), (3) Brownian motion (definition and properties), (3A) Black-Scholes model, (4) continuous-time Markov chains (Chapman-Kolmogorov equations, infinitesimal generator, birth and death Processes), (4A) Introduction of queueing modelsThe 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 stochasticly with time. The topics include: (1) discrete-time Markov chains (classification of states, periodicity, ergodic, finite-state Markov chain), (1A) hidden Markov models, (2) Poisson process (definitions and properties), (2A) non-homogeneous Poisson processes (properties and applications), (3) Brownian motion (definition and properties), (3A) Black-Scholes model, (4) continuous-time Markov chains (Chapman-Kolmogorov equations, infinitesimal generator, birth and death Processes), (4A) Introduction of queueing models
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 stochastic 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 limit and students�interests. They are:
1.Preliminaries: lack of memory property, transformations, inequalities, limit theories, 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, filters, stopping time, martingale CLT
8.Diffusion Processes: Brownian motions, It�s 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 | 3-4 assignments |
| Mid-term ExamMid-term Exam Mid-term Exam |
30 | |
| Project ReportProject Report Project Report |
40 |
