110年第1學期-1590 隨機過程 課程資訊

評分方式

Midterm Exam 33
Assignments & Learning Attitude 33
Project Report 34

教育目標

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: 0. Introduction to Stochastic Processes 1. Markov Chains 1A. Applications of MC 2. Poisson processes 2A. NHPP and extensions 3. Continuous-Time Markov Chain 3A. Applications of continuous-time MC 4. Brownian motion and Martingale 4A. Applications of Brownian motion

課程概述

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

參考書目

1. Sheldon M. Ross (2014) Introduction to Probability Models, 11th ed, Academic Press
2. Shunji Osaki (1992) Applied Stochastic System Modeling, Springer, Berlin.
3. P.W. Jones, P. Smith (2001) Stochastic Processes: An Introduction, Arnold, London.