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1、应用随机过程教学大纲“ Applied Stochastic Process ” Course Outline课程编号： 152063A 课程类型：专业选修课 总 学 时： 48讲课学时： 48 实验（上机）学时： 0学分： 3适用对象：经济学、管理学、统计学、金融学等 先修课程：概率论与数理统计、线性代数、微积分Course Code: 152063ACourse Type: Discipline basic coursePeriods: 48 Lecture: 48 Experiment （Computer）: 0Credits: 3Applicable Subjects: Economi
2、cs, Management, Statistics, Financeetc.Preparatory Courses: Probability and Mathematical Statistics,Linear Algebra, Mathematical Analysis一、课程的教学目标 这是一门向经济学和管理学相关专业本科生介绍随机过程的理论方法和实 际应用的专业选修课程。本课程在学生已经扎实掌握概率论和数理统计基础知 识的前提下，介绍随机过程中的基本概念和结果。本课程主要训练学生的如下 能力：（1）灵活组合运用微积分，线性代数和概率论解决数学问题的能力； （ 2） 进一步的抽象思维和符
3、号运算能力；（ 3）把实际问题抽象为理论模型，再把理 论结果结合实际情况进行解释的能力；（ 4）利用计算机和 MATLAB 软件解决 复杂计算问题和无解析解的问题的能力。学习完本课程后，学生们能对随机过 程及其应用有基本的认识，并且具有今后进一步学习高级随机过程理论,现代金融工程和随机控制理论和从事相关工作的专业基础。The course of Applied Stochastic Processintroduces theory and application of stochastic process to undergraduatestudents. Students are assum
4、edto have already finished their study of undergraduate level probability and statistics. Students train the following abilities this course: (1) methodologically applying calculus, linear algebra and probability theory to new mathematical problems; (2) advanced logical reasoning and symbol handling
5、; (3) building mathematical models from real world problems, and then translating mathematical results back to fit the original question; (4) employing computers and MATLAB software to solve computationally complexed problems and/or problems without closed form solution. Upon finishing the course, s
6、tudents can gain a basic understanding of the theory and application of stochastic process, and build a foundation for studying advanced stochastic process theory, modern financial engineering and stochastic control theory, as well as performing relevant work.二、教学基本要求本课程讲述随机过程的基础理论结果及其应用。 随机过程是比随机变量
7、更深 入一步的数学概念， 理解随机过程必须建立在学生扎实深入的学好概率论， 掌握 随机变量的性质的基础上。 同时，本课程还要求学生对微积分和线性代数有深刻 的掌握，并能灵活运用已有知识去解决新问题。 随机过程属于数学中较难理解的 概念，同时学生们很可能在先修课程中就有不明白的地方。 因此，任课教师需要 精心设计教学计划和编写课件， 做到能深入浅出的阐述相关理论。 同时在授课中 要及时与学生交流并发现学生知识结构中的薄弱点有针对性的进行讲解。 本课程 重点讲解随机过程中的最基本要素： 泊松过程， 更新过程和马尔科夫过程。 尽量 做到让学生对这些最重要的概念有全面深刻的了解， 从而能举一反三学习更
8、广泛 深入的知识。本课程将讲述大量例子来与理论相结合。 并计划安排少量计算机实践来向学 生解释实际中处理问题的方法。 教学中，鼓励学生课前预习， 课上安排课堂讨论， 提高学生的课堂参与积极性， 以便学生能够深入理解知识要点； 课后让学生完成 作业并对部分习题进行课堂讲解。课程的考核方式及其所占权重如下：10%20%70%出勤 作业 期末闭卷考试在上述考核方式中，作业来自于课本中的理论和实践习题；期末闭卷考试考 查理论知识和解决应用题的能力This course introduces basic results and applications of stochastic process. St
9、ochastic process lays its foundation on and is a further development of the concept of random variables. For this reason, students are expected to have already had a firm grasp of undergraduate level probability and statistic knowledge, as well as calculus and linear algebra. Students should also be
10、 able to use what they already have known methodologically to solve new problems. Stochastic process falls into the category of “hard ”mathematics for undergraduate level students. On the other hand, most undergraduatestudents have difficulties understanding at least certain mathematical knowledge t
11、hey have already learned. Under these circumstances, the lecturer is required to carefully design the structure of instruction and the lecture notes to ensure hard concepts are instilled step by step following special examples and concepts easier to understand. During the instruction, the lecturer s
12、hould be keen to spot weak points of students knowledge structure and clear the obstacle hindering progress. Thecourse is built around three fundamental concepts in stochastic process: Poisson process, renewal process and Markov process. Once students are able to comprehend those seminal building bl
13、ocks, they will explore other vast areas of this subject much faster.The course will introduce numerous examples along with theory knowledge. Students are encouraged to read relevant materials before the class. Discussions will be organized in the class to facilitate better understanding. Problem se
14、ts is given after class, and some of them will be analyzed in later classes.The methods of evaluation of this course and their weights are as follows:10%20%70%Atte ndanceAssig nmentsFinal Exam (closed)In the methods of evaluation above, the assignments comefrom the theoretical and application exerci
15、ses in the textbook. The closed form final exam focuses on the exam in ati on of kno wledge in theory.三、各教学环节学时分配教学课时分配序号早节内谷讲课实验其他合计绪论In troductio n11概率论回顾Review of ProbabilityTheory22泊松过程Poiss on Process415非齐次泊松过程Non homoge neous Poiss onProcess213复合泊松过程Compo und Poiss on Process22排队论基础Eleme ntary Queu ing Theory314泊松到达平均Poiss on Arrival See TimeAverage11数列的生成函数The gen erat ing function of aSequenee11更新过程Ren ewal Process819剩余寿命，当前寿命和总观 测寿命Excess Life, Current Life and Total Life617离散马尔科夫链Discrete-time MarkovChai ns617连续马尔科夫链Con
