# 98年第1學期-4850 隨機過程 課程資訊

## 評分方式

Mid-term exam 30
Final exam 30
Assignments and workshops 40

## 教育目標

The objective of this course is to introduce basic concepts for stochastic processes. We will focus on studying probabilistic models. Students will learn concepts and techniques for characterizing models stochastically. Background on probability and mathematical statistics are necessary. The topics of this course include basic processes, stochastic models, and diffusion processes. Contents are: 1.Preliminaries 2.Markov chains 3.Poisson processes 4.Continuous-time Markov chains 5.Renewal processes 6.Stochastic models 7.Martingales 8.Brownian motions and diffusion processes

## 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. Shunji Osaki (1992) Applied Stochastic System Modeling, Springer, Berlin.
2. Samuel Karlin, Howard M. Taylor (1975) A First Course in Stochastic Processes, 2nd edn, Academic Press, New York.
3. Sheldon M. Ross (1996) Stochastic Processes, 2nd edn, John Wiley , New York.
4. P.W. Jones, P. Smith (2001) Stochastic Processes: An Introduction, Arnold, London.