随机过程教学大纲Stochastic Processes SubjectSyllabus，课程信息SubjectInformation课程编号：开课学期：53100313010SubjectSemesterID课程分所属课群：类：专业方向类课程SectionCategory课程学分:总学时/周：3.556CreditTotalHours/WeeksPoints理论学时;实验学时：560LECT.EXP.HoursHoursPBL学时:实践学时/周：00PBLPRAC. Hours/WeeksHours开课学适用专业：院：悉尼智能科技学院应用统计学ASStreamCollege课程属课程模式：性：必修Compulsory引进UTSModePattern中方课程协调成绩记载方式：人:张永超，胡海娟百分制MarksResult TypeNEU Coordinator先修课程：数学分析与建模导论，概率论与随机变量，微分方程RequisitesElementsofStochasticModelling[Borokov,2014]英文参考教材：ABenchmarkApproachtoQuantitativeFinance[PlatenandHeath,2006]ENStochastic Calculus for Finance I [Shreve, 2005]TextbooksStochasticCalculusforFinanceII[Shreve,2004](advanced)1/11
1 / 11 随机过程 教学大纲 Stochastic Processes Subject Syllabus 一、课程信息 Subject Information 课程编 号: Subject ID 3100313010 开课学期: Semester 5 课程分 类: Category 所属课群: Section 专业方向类课程 课程学 分: Credit Points 3.5 总学时/周: Total Hours/Weeks 56 理论学 时: LECT. Hours 56 实验学时: EXP. Hours 0 PBL 学 时: PBL Hours 0 实践学时/周: PRAC. Hours/Weeks 0 开课学 院: College 悉尼智能科技学院 适用专业: Stream 应用统计学 AS 课程属 性: Pattern 必修 Compulsory 课程模式: Mode 引进 UTS 中方课 程协调 人: NEU Co ordinator 张永超，胡海娟 成绩记载方式: Result Type 百分制 Marks 先修课 程: Requisit es 数学分析与建模导论，概率论与随机变量，微分方程 英文参 考教材: EN Textboo ks Elements of Stochastic Modelling [Borokov, 2014] A Benchmark Approach to Quantitative Finance [Platen and Heath, 2006] Stochastic Calculus for Finance I [Shreve, 2005] Stochastic Calculus for Finance II [Shreve, 2004] (advanced)
FinancialModellingwithJumpProcessesContandTankov,2o04/(advanced)中文参考教材：无CN Textbooks教学资https:/lms.cloudcampus.com.cn/login/canvas源：https://canvas.uts.edu.au/courses/22701/pages/computational-software?module_item_iResourced=862426S课程负责人(撰提交日期：单击或点击此处输入写人):张永超日期。Submitted DateSubjectDirector任课教师(含负责人）张永超，胡海娟Taughtby审核人：批准人：韩鹏Checked史闻博Approvedbyby批准日期：单击或点击此处输入日期。ApprovedDate2 / 11
2 / 11 Financial Modelling with Jump Processes [Cont and Tankov, 2004] (advanced) 中文参 考教材: CN Text books 无 教学资 源: Resource s https://lms.cloudcampus.com.cn/login/canvas https://canvas.uts.edu.au/courses/22701/pages/computational-software?module_item_i d=862426 课程负 责人(撰 写人): SubjectD irector 张永超 提交日期: Submitted Date 单击或点击此处输入 日期。 任课教 师(含负 责人): Taught by 张永超，胡海娟 审核人: Checked by 韩鹏 批准人: Approvedby 史闻博 批准日期: Approved Date 单击或点击此处输入 日期
二、教学目标SubjectLearningObjectives(SLOs)注：毕业要求及指标点可参照悉尼学院本科生培养方案，可根据实际情况增减行数Note: GA and index can be referred from undergraduate program in SSTC website. Please add/reduce lines based on subject展示数学科学的理论和技术知识，包括微积分、离散数学、线性代数、概率、统计学和定量管理。评估解决问题、分析、应用和批判性思维的数学和统计方法，以进行数学论证，并基于分析、数值、统计算法进行实验，以解决新问题。整体目标：Demonstrate theoretical andtechnical knowledge of mathematicalOverall Objectivesciences including calculus, discrete mathematics, linear algebra,probability,statistics and quantitative management.Evaluate mathematical and statistical approaches to problem solving,analysis, application, and critical thinking to make mathematicalarguments, and conduct experiments based on analytical, numerical,statistical,algorithmstosolvenewproblems.定义并说明概率和随机过程中使用的术语。1-1Define and illustrate the terms used in probability andstochasticprocesses讨论和演示概率中使用的证明技术以及随机过程理论中重要的一些数学推导。1-2Discuss and demonstrate the techniques of proof used inprobability and some of the mathematical derivations that areimportant in the theoryof stochastic processes陈述并应用概率的基本极限定理。1-3State and apply the basic limit theorems of probability展示使用数学技术分析各种随机过程行为的能力，尤其是（1）专业目标：长期或稳态行为。Professional Ability1-4Demonstrate an ability to usemathematical techniques toanalyse the behaviour of various stochastic processesespecially the long-run or steady state behaviour制定和解决涉及概率和随机过程的应用和理论问题。1-5Formulateand solveappliedand theoretical problemsinvolving probability and stochastic processes清楚地传达概率和随机进程主题的知识以及涉及这些主题的问题的解决方案。1-6Communicateclearlyknowledgeof the subject matter ofprobabilityandstochasticprocessesandsolutions toproblems involving these topics自主工作或团队合作，展示对需要应用数学和统计学的现实生活问题的专业和负责任的分析。2-1Workautonomouslyorinteamstodemonstrateprofessional（2）德育目标：and responsible analysis of real-life problemsthat requireEssential Qualityapplicationofmathematicsandstatistics使用各种方法，简洁准确地表达推理和结论，向各种受众2-2传达数学解决方案及其含义。3/ 11
3 / 11 二、教学目标 Subject Learning Objectives (SLOs) 注：毕业要求及指标点可参照悉尼学院本科生培养方案，可根据实际情况增减行数 Note: GA and index can be referred from undergraduate program in SSTC website. Please add/reduce lines based on subject. 整体目标: Overall Objective 展示数学科学的理论和技术知识，包括微积分、离散数学、线性代 数、概率、统计学和定量管理。 评估解决问题、分析、应用和批判性思维的数学和统计方法，以进 行数学论证，并基于分析、数值、统计算法进行实验，以解决新问 题。 Demonstrate theoretical and technical knowledge of mathematical sciences including calculus, discrete mathematics, linear algebra, probability, statistics and quantitative management. Evaluate mathematical and statistical approaches to problem solving, analysis, application, and critical thinking to make mathematical arguments, and conduct experiments based on analytical, numerical, statistical, algorithms to solve new problems. （1）专业目标: Professional Ability 1-1 定义并说明概率和随机过程中使用的术语。 Define and illustrate the terms used in probability and stochastic processes. 1-2 讨论和演示概率中使用的证明技术以及随机过程理论中 重要的一些数学推导。 Discuss and demonstrate the techniques of proof used in probability and some of the mathematical derivations that are important in the theory of stochastic processes. 1-3 陈述并应用概率的基本极限定理。 State and apply the basic limit theorems of probability. 1-4 展示使用数学技术分析各种随机过程行为的能力，尤其是 长期或稳态行为。 Demonstrate an ability to use mathematical techniques to analyse the behaviour of various stochastic processes, especially the long-run or steady state behaviour. 1-5 制定和解决涉及概率和随机过程的应用和理论问题。 Formulate and solve applied and theoretical problems involving probability and stochastic processes 1-6 清楚地传达概率和随机进程主题的知识以及涉及这些主 题的问题的解决方案。 Communicate clearly knowledge of the subject matter of probability and stochastic processes and solutions to problems involving these topics. （2）德育目标: Essential Quality 2-1 自主工作或团队合作，展示对需要应用数学和统计学的现 实生活问题的专业和负责任的分析。 Work autonomously or in teams to demonstrate professional and responsible analysis of real-life problems that require application of mathematics and statistics. 2-2 使用各种方法，简洁准确地表达推理和结论，向各种受众 传达数学解决方案及其含义
Use succinct and accurate presentation of reasoning andconclusions to communicatemathematical solutions,andtheir implications, to a variety of audiences, using a varietyofapproaches.课程教学目标与毕业要求的对应关系MatrixofGA&SLOs毕业要求GA指标点GAIndex教学目标SLOs指标点1-1：具有较强的演绎推理能力、1、理学知识：具有扎实的数学准确计算能力、分析归纳能力、抽象思基础，能够将数学、自然科学1-1—1-6维能力，掌握数学、自然科学和相关专和专业知识用于解决复杂实际业知识，并使用其建立正确的数学、物问题。理学等模型以解释复杂实际问题。5、使用现代工具：能够针对复杂实际问题，开发、选择与使指标点5-3：能够针对本专业相关复杂用恰当的技术、资源、现代信实际问题，选择与使用恰当的技术、资2-1, 2-2息技术工具，包括对复杂实际源、现代信息技术工具。问题的预测与模拟，并能够理解其局限性。三、教学内容Content(Topics)注：以中英文填写，各部分内容的表格可根据实际知识单元数量进行复制、扩展或缩减Note: Filled in both CN and EN, extend or reduce based on the actual numbers of knowledge unit(1)理论教学Lecture知识单元序号：支撑教学目标：11-1,1-2,1-6,2-2Knowledge Unit No.SLOs Supported知识单元名称公理化方法介绍，概率基础IntroductiontoaxiomaticapproachUnit Titleprobabilitybasics概率论历史Historyofprobabilitytheory频率方法Frequencyapproachtoprobability知识点：Kolmogorov公理化方法IntroductiontoKolmogorovsaxiomaticKnowledge Deliveryapproach条件概率与独立事件Conditionalprobabilityandindependentevents随机变量ScalarRVs了解：概率论历史HistoryofprobabilitytheoryRecognize频率方法、Kolmogorov公理化方法Frequency理解：学习目标approach to probability,Introduction to Kolmogorov'sUnderstandLearning Objectivesaxiomaticapproach掌握：条件概率与独立事件、随机变量ConditionalMasterprobability and independent events,ScalarRVs使用各种方法，简洁准确地表达推理和结论，向各种受众传达数学德育目标解决方案及其含义。Moral ObjectivesUse succinctand accuratepresentationofreasoningandconclusionsto4/11
4 / 11 Use succinct and accurate presentation of reasoning and conclusions to communicate mathematical solutions, and their implications, to a variety of audiences, using a variety of approaches. 课程教学目标与毕业要求的对应关系 Matrix of GA & SLOs 毕业要求 GA 指标点 GA Index 教学目标 SLOs 1、理学知识：具有扎实的数学 基础，能够将数学、自然科学 和专业知识用于解决复杂实际 问题。 指标点 1-1：具有较强的演绎推理能力、 准确计算能力、分析归纳能力、抽象思 维能力，掌握数学、自然科学和相关专 业知识，并使用其建立正确的数学、物 理学等模型以解释复杂实际问题。 1-1—1-6 5、使用现代工具：能够针对复 杂实际问题，开发、选择与使 用恰当的技术、资源、现代信 息技术工具，包括对复杂实际 问题的预测与模拟，并能够理 解其局限性。 指标点 5-3：能够针对本专业相关复杂 实际问题，选择与使用恰当的技术、资 源、现代信息技术工具。 2-1，2-2 三、教学内容 Content (Topics) 注：以中英文填写，各部分内容的表格可根据实际知识单元数量进行复制、扩展或缩减 Note: Filled in both CN and EN, extend or reduce based on the actual numbers of knowledge unit (1) 理论教学 Lecture 知识单元序号: Knowledge Unit No. 1 支撑教学目标: SLOs Supported 1-1，1-2，1-6，2-2 知识单元名称 Unit Title 公理化方法介绍，概率基础 Introduction to axiomatic approach, probability basics 知识点: Knowledge Delivery 概率论历史 History of probability theory 频率方法 Frequency approach to probability Kolmogorov 公理化方法 Introduction to Kolmogorov’s axiomatic approach 条件概率与独立事件 Conditional probability and independent events 随机变量 Scalar RVs 学习目标: Learning Objectives 了解: Recognize 概率论历史 History of probability theory 理解: Understand 频率方法、 Kolmogorov 公理化方法 Frequency approach to probability，Introduction to Kolmogorov’s axiomatic approach 掌握: Master 条件概率与独立事件、随机变量 Conditional probability and independent events，Scalar RVs 德育目标 Moral Objectives 使用各种方法，简洁准确地表达推理和结论，向各种受众传达数学 解决方案及其含义。 Use succinct and accurate presentation of reasoning and conclusions to
communicate mathematical solutions, and their implications, to avariety of audiences, using a variety of approaches.重点：条件概率与独立事件、随机变量ConditionalprobabilityandKey Pointsindependent events, Scalar RVs难点：Kolmogorov公理化方法，IntroductiontoKolmogorov's axiomaticFocal pointsapproach知识单元序号：支撑教学目标21-1,1-2,1-6, 2-2Knowledge Unit No.SLOs Supported知识单元名称多元Gauss随机变量MultivariateGaussian randomvariablesUnit TitleGauss随机向量的构造ConstructingGaussianvectorRVs知识点：Gauss随机向量的仿射变换Affine-lineartransformof GaussianKnowledge Deliveryvector RVs正态相关定理Theoremonnormalcorrelation了解:Recognize理解:学习目标：UnderstandLearning ObjectivesGauss随机向量的构造、Gauss随机向量的仿射变换、掌握：正态相关定理ConstructingGaussianvectorRVs，MasterAffine-linear transform of Gaussian vector RVs,Theorem onnormal correlation使用各种方法，简洁准确地表达推理和结论，向各种受众传达数学解决方案及其含义。德育目标Use succinct andaccuratepresentation of reasoningand conclusions toMoral Objectivescommunicate mathematical solutions,andtheir implications,toavarietyof audiences,using a variety ofapproaches.Gauss随机向量的构造、Gauss随机向量的仿射变换、正态相关定重点：理 Constructing Gaussian vectorRVs，Affine-lineartransform ofKey PointsGaussianvectorRVs,Theoremon normal correlation难点：正态相关定理TheoremonnormalcorrelationFocal points知识单元序号：支撑教学目标：1-1,1-2，1-3,1-6,3SLOs Supported2-1, 2-2KnowledgeUnitNo知识单元名称随机模拟方法MethodsofstochasticsimulationUnit Title随机变量的收敛性ConvergenceofRVs知识点：极限定理LimittheoremsKnowledge Delivery随机模拟Stochasticsimulation随机变量的随机模拟SimulationofRVs了解：学习目标：随机变量的收敛性ConvergenceofRVsRecognizeLearning Objectives理解：极限定理、随机模拟LimittheoremsStochastic5 /11
5 / 11 communicate mathematical solutions, and their implications, to a variety of audiences, using a variety of approaches. 重点: Key Points 条件概率与独立事件、随机变量 Conditional probability and independent events，Scalar RVs 难点: Focal points Kolmogorov 公理化方法，Introduction to Kolmogorov’s axiomatic approach 知识单元序号: Knowledge Unit No. 2 支撑教学目标: SLOs Supported 1-1，1-2，1-6，2-2 知识单元名称 Unit Title 多元 Gauss 随机变量 Multivariate Gaussian random variables 知识点: Knowledge Delivery Gauss 随机向量的构造 Constructing Gaussian vector RVs Gauss 随机向量的仿射变换 Affine-linear transform of Gaussian vector RVs 正态相关定理 Theorem on normal correlation 学习目标: Learning Objectives 了解: Recognize 理解: Understand 掌握: Master Gauss 随机向量的构造、Gauss 随机向量的仿射变换、 正态相关定理 Constructing Gaussian vector RVs， Affine-linear transform of Gaussian vector RVs ， Theorem on normal correlation 德育目标 Moral Objectives 使用各种方法，简洁准确地表达推理和结论，向各种受众传达数学 解决方案及其含义。 Use succinct and accurate presentation of reasoning and conclusions to communicate mathematical solutions, and their implications, to a variety of audiences, using a variety of approaches. 重点: Key Points Gauss 随机向量的构造、Gauss 随机向量的仿射变换、正态相关定 理 Constructing Gaussian vector RVs，Affine-linear transform of Gaussian vector RVs，Theorem on normal correlation 难点: Focal points 正态相关定理 Theorem on normal correlation 知识单元序号: Knowledge Unit No. 3 支撑教学目标: SLOs Supported 1-1，1-2，1-3，1-6， 2-1，2-2 知识单元名称 Unit Title 随机模拟方法 Methods of stochastic simulation 知识点: Knowledge Delivery 随机变量的收敛性 Convergence of RVs 极限定理 Limit theorems 随机模拟 Stochastic simulation 随机变量的随机模拟 Simulation of RVs 学习目标: Learning Objectives 了解: Recognize 随机变量的收敛性 Convergence of RVs 理解: 极限定理、随机模拟 Limit theorems， Stochastic