11310 隨機過程

# Electives # Graduate Program # Information & Operations Research
5 Lectures / 43 Sections / 14h 45m 27s
Lecture 1：Course Introduction
Lecture 2：Conditional Probability and Exceptation
Section 1
20:44
Section 2
57:21
Section 3
01:00:17
Section 4
14:24
Section 5
10:13
Section 6
15:29
Section 7
13:53
Lecture 3：Markov Chains
Section 1
14:59
Section 2
10:59
Section 3
27:48
Section 4
12:45
Section 5
16:01
Section 6
41:59
Section 7
13:52
Section 8
13:53
Section 9
25:58
Lecture 4：The Exponential Distribution and the Poisson Process
Section 1
19:03
Section 2
10:00
Section 3
30:51
Section 4
21:52
Section 5
15:25
Section 6
09:44
Section 7
08:05
Section 8
10:57
Section 9
29:40
Section 10
14:49
Section 11
10:51
Section 12
06:35
Section 13
08:25
Section 14
22:08
Section 15
28:59
Section 16
15:01
Section 17
10:28
Lecture 5：Continuous-Time Markov Chains
Section 1
09:45
Section 2
39:10
Section 3
09:46
Section 4
13:11
Section 5
20:26
Section 6
26:35
Introduction
Duration｜ 14h 45m 27s
Total Lectures｜ 5 Lectures 43 Sections

Brief course descriptions

This course is for students to achieve the following goals: To develop an ability to model dynamical processes as stochastic processes; To develop an understanding of important qualitative characteristics of stochastic processes; To develop an ability to analyze basic stochastic processes.

Course keywords

高等機率, 隨機模式, 高等統計, 模擬, 馬可夫鏈

Prerequisites

IEEM203000 (Engineering Statistics) or equivalent basic probability course.

Textbook

Introduction to Probability Models, 10th Ed. by Sheldon M. Ross, Academic Press, 2009 (or the newest version).

Course Topics

Chapter 3. Conditional Probability and Conditional Expectation

Chapter 4. Markov Chains

Chapter 5. The Exponential Distribution and the Poisson process

Chapter 6. Continuous-time Markov Chain (CTMC)

Chapter 7. Renewal theory and its applications

Chapter 8. Queueing Theory

Lectures
Lecture 1：Course Introduction
Section 1 - Outline of the course
21:03
Section 2 - Preliminaries
28:17
Section 3 - Preliminaries (2)
48:15
Section 4 - Basic Nature of Stochastic Processes, Explanation of Lecture Materials
25:31
Lecture 2：Conditional Probability and Exceptation
Section 1 - Conditional Probability and conditional pdf
20:44
Section 2 - Examples and Exercise Problems
57:21
Section 3 - More Examples (Reliability)
01:00:17
Section 4 - The Ballot Problem
14:24
Section 5 - More about Conditional Expectation and Example
10:13
Section 6 - Some Probability Inequalities
15:29
Section 7 - Limit Theorems
13:53
Lecture 3：Markov Chains
Section 1 - Definition, Terminologies and Examples
14:59
Section 2 - Chapman-Kolmogorov Equations and Examples
10:59
Section 3 - Uncondtional Distribution of the State at Time n, Classification of States, Examples
27:48
Section 4 - Proposition, Corollary and Examples
12:45
Section 5 - The Gambler's Ruin Problem
16:01
Section 6 - 1D-Random Walk, 2D-Random Walk
41:59
Section 7 - 2D-Random Walk (2)
13:52
Section 8 - 1D Inhomogeneous Random Walk
13:53
Section 9 - Limiting Probabilities (Stationary Distribution), Periodicity
25:58
Lecture 4：The Exponential Distribution and the Poisson Process
Section 1 - Introduction of Exponential Distribution
19:03
Section 2 - Properties of Exponential Distribution
10:00
Section 3 - Examples and a Further Question
30:51
Section 4 - Hyperexponential Distribution and More about the Exponential Distribution
21:52
Section 5 - Convelution of Exponential Random Variables, Proposition
15:25
Section 6 - Counting Process and Poisson Process
09:44
Section 7 - Theorem of Poisson Process
08:05
Section 8 - Definition, Another Way to Define Poisson Process, Interarrival and Waiting Time Distributions
10:57
Section 9 - Further Properties of Poisson Process, the Coupon Collecting Process
29:40
Section 10 - Continuation of the Coupon Collecting Process
14:49
Section 11 - Question involving two Poisson processes
10:51
Section 12 - Conditional Distribution of the Arrival Times
06:35
Section 13 - Remark about the Conditional Distribution of the Arrival Times
08:25
Section 14 - Sampling a Poisson Process, Example of an Infinite Server Queue
22:08
Section 15 - More Examples
28:59
Section 16 - Nonhomogeneous Poisson Process
15:01
Section 17 - Compound Poisson Process
10:28
Lecture 5：Continuous-Time Markov Chains
Section 1 - Introduction
09:45
Section 2 - Birth and Death Processes
39:10
Section 3 - A General Birth and Death Process
09:46
Section 4 - The Transition Probability Function, Lemma
13:11
Section 5 - Chapman-Kolmogorov Equations
20:26
Section 6 - Kolmogorov's Forward Equations
26:35
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Prof. Chang Kuo-Hao
Prof. Chang Kuo-Hao

Dept. Industrial Engineering and Engineering Management

Research Field

Big Data Analytics; Stochastic Optimization; Monte Carlo Simulation; Applied Probability and Statistics

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