东北大学：某学院应用统计学专业《随机过程》课程教学大纲

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

Understandsimulation掌握：随机变量的随机模拟SimulationofRVsMaster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。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WorkautonomouslyorinteamstodemonstrateprofessionalandMoral Objectivesresponsibleanalysisofreal-lifeproblemsthatrequireapplicationofmathematics and statistics.Usesuccinctandaccuratepresentation of reasoning and conclusions tocommunicate mathematical solutions,andtheir implications,to avariety ofaudiences,usinga varietyof approaches.重点：随机变量的随机模拟SimulationofRVsKey Points难点：随机变量的收敛性、随机模拟ConvergenceofRVs，StochasticFocal pointssimulation知识单元序号：支撑教学目标：1-1,1-2,1-4,1-5,4Knowledge Unit No.SLOs Supported1-6, 2-2随机过程介绍，Gauss随机过程，平稳随机过程Introductionto知识单元名称stochasticprocesses,Gaussian SPs,stationarySPsUnit Title般定义Generaldefinitions知识点：Gauss过程GaussianprocessesKnowledge Delivery平稳过程Stationaryprocesses了解：Recognize理解：学习目标：-般定义GeneraldefinitionsLearning ObjectivesUnderstand掌握：Gauss过程、平稳过程Gaussianprocesses，StationaryMasterprocesses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 and accuratepresentation of reasoning and conclusions toMoral Objectivescommunicate mathematical solutions, and their implications,to avarietyofaudiences,usingavarietyofapproaches.重点：Gauss过程GaussianprocessesKey Points难点：Gauss过程GaussianprocessesFocal points知识单元序号支撑教学目标：1-1, 1-2, 1-4,1-5,5SLOs Supported1-6, 2-2Knowledge UnitNo知识单元名称Markov过程，离散时间Markov链Markovprocesses，discrete-time6/11

6 / 11 Understand simulation 掌握: Master 随机变量的随机模拟 Simulation of RVs 德育目标 Moral Objectives 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。 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。 Work autonomously or in teams to demonstrate professional and responsible analysis of real-life problems that require application of mathematics and statistics. 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 随机变量的随机模拟 Simulation of RVs 难点: Focal points 随机变量的收敛性、随机模拟 Convergence of RVs， Stochastic simulation 知识单元序号: Knowledge Unit No. 4 支撑教学目标: SLOs Supported 1-1，1-2，1-4，1-5， 1-6，2-2 知识单元名称 Unit Title 随机过程介绍，Gauss 随机过程，平稳随机过程 Introduction to stochastic processes，Gaussian SPs，stationary SPs 知识点: Knowledge Delivery 一般定义 General definitions Gauss 过程 Gaussian processes 平稳过程 Stationary processes 学习目标: Learning Objectives 了解: Recognize 理解: Understand 一般定义 General definitions 掌握: Master Gauss 过程、平稳过程 Gaussian processes，Stationary processes 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 过程 Gaussian processes 难点: Focal points Gauss 过程 Gaussian processes 知识单元序号: Knowledge Unit No. 5 支撑教学目标: SLOs Supported 1-1，1-2，1-4，1-5， 1-6，2-2 知识单元名称 Markov 过程，离散时间 Markov 链 Markov processes，discrete-time

Unit TitleMarkov chains定义和一般性质Definitionandgeneralproperties知识点：Gauss Markov 过程Gaussian Markov processesKnowledge DeliveryChapman-Kolmogorov方程Chapman-Kolmogorovequations离散时间齐次Markov链Discrete-timehomogenousMarkovchains了解:Recognize理解：定义和一般性质Definitionandgeneral properties学习目标：UnderstandLearning ObjectivesGaussMarkov过程、Chapman-Kolmogorov方程、离掌握：散时间齐次Markov链、GaussianMarkovprocesses，MasterChapman-Kolmogorovequations,Discrete-timehomogenous Markov chains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 and accurate presentation of reasoning and conclusions toMoral Objectivescommunicate mathematical solutions,and their implications,to avariety of audiences,using a variety of approaches.重点：GaussMarkov过程、离散时间齐次Markov链GaussianMarkovKey PointsDiscrete-timehomogenous Markov chainsprocesses，难点：路由算法的意义及评价Focal points知识单元序号支撑教学目标：1-1,1-2,1-4,1-5,6Knowledge Unit No.SLOs Supported1-6, 2-2连续时间Markov链，复合Poisson过程Continuous-timeMarkov知识单元名称chains，compoundPoissonprocessesUnit Title连续时间齐次Markov链Continuous-timehomogenous Markov知识点：chainsKnowledge Delivery复合Poisson过程CompoundPoissonprocesses了解：Recognize理解：学习目标：UnderstandLearning Objectives连续时间齐次Markov链、复合Poisson过程掌握：Continuous-timeMarkovchainshomogenousMasterCompound Poisson processes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 and accurate presentation of reasoning and conclusions toMoral Objectivescommunicate mathematical solutions, and their implications,to avariety ofaudiences, using a variety of approaches.重点：连续时间齐次Markov链、复合Poisson过程Continuous-timeKey PointshomogenousMarkovchains,CompoundPoissonprocesses7/11

7 / 11 Unit Title Markov chains 知识点: Knowledge Delivery 定义和一般性质 Definition and general properties Gauss Markov 过程 Gaussian Markov processes Chapman-Kolmogorov 方程 Chapman-Kolmogorov equations 离散时间齐次 Markov 链 Discrete-time homogenous Markov chains 学习目标: Learning Objectives 了解: Recognize 理解: Understand 定义和一般性质 Definition and general properties 掌握: Master Gauss Markov 过程、Chapman-Kolmogorov 方程、离 散时间齐次 Markov 链、Gaussian Markov processes ， Chapman-Kolmogorov equations ， Discrete-time homogenous Markov chains 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 Markov 过程、离散时间齐次 Markov 链 Gaussian Markov processes ，Discrete-time homogenous Markov chains 难点: Focal points 路由算法的意义及评价 知识单元序号: Knowledge Unit No. 6 支撑教学目标: SLOs Supported 1-1，1-2，1-4，1-5， 1-6，2-2 知识单元名称 Unit Title 连续时间Markov链，复合Poisson过程Continuous-time Markov chains，compound Poisson processes 知识点: Knowledge Delivery 连续时间齐次 Markov 链 Continuous-time homogenous Markov chains 复合 Poisson 过程 Compound Poisson processes 学习目标: Learning Objectives 了解: Recognize 理解: Understand 掌握: Master 连 续 时 间 齐 次 Markov 链 、 复 合 Poisson 过 程 Continuous-time homogenous Markov chains ， Compound Poisson processes 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 连续时间齐次 Markov 链、复合 Poisson 过程 Continuous-time homogenous Markov chains， Compound Poisson processes

难点：连续时间齐次Markov链、复合Poisson 过程Continuous-timeFocal pointshomogenousMarkovchains,CompoundPoissonprocesses知识单元序号：支撑教学目标：1-1,1-2, 1-4, 1-5,7SLOs SupportedKnowledge Unit No1-6,2-2知识单元名称ARMA过程ARMAprocessesUnit Title定义、动机Definitions，Motivation虑子Filters知识点：移位算子演算Calculusof shiftoperator平稳性StationarityKnowledge Delivery因果性和可逆性Causalityand invertibility非平稳性Non-stationarity了解：定义、动机Definitions，MotivationRecognize学习目标：理解：虑子、因果性和可逆性、非平稳性Filters，CausalityLearning ObjectivesUnderstandand invertibility,Non-stationarity掌握：移位算子演算、平稳性Calculusof shiftoperator，MasterStationarity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 succinctand accuratepresentationof reasoning and conclusionstoMoral Objectivescommunicate mathematical solutions, and their implications, to avariety of audiences, using a variety of approaches.重点：移位算子演算、平稳性Calculusofshiftoperator，StationarityKey Points难点：移位算子演算Calculus of shiftoperatorFocal points知识单元序号支撑教学目标：1-1,1-2,1-4,1-5,8Knowledge Unit No.SLOs Supported1-6, 2-2扩撤过程基础，随机积分，Ito公式Elementsofdiffusion知识单元名称processes，stochasticintegration，ItoformulaUnit Title定义Definitions转移密度Transitiondensities知识点：Black-Scholes模型中的Kolmogorov向后方程KolmogorovKnowledge Deliverybackward equation in Black-Scholes model关于Brown运动的随机积分Stochastic integrals withrespecttoBrownian motion了解：Recognize学习目标：理解：Learning Objectives定义、转移密度Definitions，TransitiondensitiesUnderstand掌握：Black-Scholes模型中的Kolmogorov向后方程、关于8/11

8 / 11 难点: Focal points 连续时间齐次 Markov 链、复合 Poisson 过程 Continuous-time homogenous Markov chains， Compound Poisson processes 知识单元序号: Knowledge Unit No. 7 支撑教学目标: SLOs Supported 1-1，1-2，1-4，1-5， 1-6，2-2 知识单元名称 Unit Title ARMA 过程 ARMA processes 知识点: Knowledge Delivery 定义、动机 Definitions，Motivation 虑子 Filters 移位算子演算 Calculus of shift operator 平稳性 Stationarity 因果性和可逆性 Causality and invertibility 非平稳性 Non-stationarity 学习目标: Learning Objectives 了解: Recognize 定义、动机 Definitions，Motivation 理解: Understand 虑子、因果性和可逆性、非平稳性 Filters， Causality and invertibility， Non-stationarity 掌握: Master 移位算子演算、平稳性 Calculus of shift operator， Stationarity 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 移位算子演算、平稳性 Calculus of shift operator，Stationarity 难点: Focal points 移位算子演算 Calculus of shift operator 知识单元序号: Knowledge Unit No. 8 支撑教学目标: SLOs Supported 1-1，1-2，1-4，1-5， 1-6，2-2 知识单元名称 Unit Title 扩撒过程基础，随机积分，Ito 公式 Elements of diffusion processes，stochastic integration，Ito formula 知识点: Knowledge Delivery 定义 Definitions 转移密度 Transition densities Black-Scholes 模 型 中 的 Kolmogorov 向 后 方 程 Kolmogorov backward equation in Black-Scholes model 关于 Brown 运动的随机积分 Stochastic integrals with respect to Brownian motion 学习目标: Learning Objectives 了解: Recognize 理解: Understand 定义、转移密度 Definitions，Transition densities 掌握: Black-Scholes 模型中的 Kolmogorov 向后方程、关于

MasterBrown运动的随机积分Kolmogorovbackwardequation in Black-Scholes model, Stochastic integralswith respect to Brownian motion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 and accurate presentation of reasoning and conclusions toMoral Objectivescommunicate mathematical solutions, and their implications, to avariety ofaudiences,using a varietyofapproaches.重点：关于Brown运动的随机积分StochasticintegralswithrespecttoKey PointsBrownianmotion难点：关于Brown运动的随机积分StochasticintegralswithrespecttoFocal pointsBrownianmotion四、教学安排TeachingSchedule注：可根据实际情况增减行数Note:Please add/reduce lines based on subject学时(周)Hour(Week)教学内容TeachingContent理论实验课外实践集中实践PBLLECT.EXP.PRAC.公理化方法介绍，概率基础Introductionto6axiomatic approach,probabilitybasics多元Gauss随机变量MultivariateGaussianrandom8variables随机模拟方法Methodsof stochasticsimulation6随机过程介绍，Gauss随机过程，平稳随机过程8Introductiontostochasticprocesses,GaussianSPsstationary SPsMarkov过程，离散时间Markov链Markov8processes,discrete-timeMarkovchains连续时间Markov链，复合Poisson过程8Continuous-timeMarkovchains,compoundPoissonprocesses6ARMA过程ARMAprocesses扩撤过程基础，随机积分，Ito公式Elementsof6diffusion processes, stochastic integration, Itoformula56总计Total五、教学方法TeachingMethodology9/11

9 / 11 Master Brown 运动的随机积分 Kolmogorov backward equation in Black-Scholes model，Stochastic integrals with respect to Brownian motion 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 关于 Brown 运动的随机积分 Stochastic integrals with respect to Brownian motion 难点: Focal points 关于 Brown 运动的随机积分 Stochastic integrals with respect to Brownian motion 四、教学安排 TeachingSchedule 注：可根据实际情况增减行数 Note: Please add/reduce lines based on subject. 教学内容 Teaching Content 学时(周)Hour(Week) 理论 LECT. 实验 EXP. 课外实践 PBL 集中实践 PRAC. 公理化方法介绍，概率基础 Introduction to axiomatic approach, probability basics 6 多元 Gauss 随机变量 Multivariate Gaussian random variables 8 随机模拟方法 Methods of stochastic simulation 6 随机过程介绍，Gauss 随机过程，平稳随机过程 Introduction to stochastic processes，Gaussian SPs， stationary SPs 8 Markov 过程，离散时间 Markov 链 Markov processes，discrete-time Markov chains 8 连续时间 Markov 链，复合 Poisson 过程 Continuous-time Markov chains，compound Poisson processes 8 ARMA 过程 ARMA processes 6 扩撒过程基础，随机积分，Ito 公式 Elements of diffusion processes ， stochastic integration ， Ito formula 6 总计 Total 56 五、教学方法 Teaching Methodology

注：可根据实际情况增减行数或修改内容Note: Please add/reduce linesor revise content based on subject勾选Check教学方法与特色TeachingMethodology&Characters多媒体教学：基于信息化设备的课堂教学团Multi-media-basedlecturing实践能力传授：理论与行业、实际案例相结合团Combiningtheorywith industrialpracticalproblems课程思政建设：知识讲授与德育相结合团KnowledgedeliverywithethiceducationPBL教学：问题驱动的分组学习与交流口Problem-basedlearning其他：单击或点击此处输入文字。口Other:单击或点击此处输入文字。六、成绩评定Assessment注：可根据实际情况增减行数或修改内容Note: Please add/reduce linesor revise content based on subject.考核环节：环节负责人：平时Behavior张永超，胡海娟DirectorAssessment Content给分形式课程总成绩比重(%)：50百分制MarksResult TypePercentage (%)出勒100分，每次考勒计10分，缺勤不得分，缺勒五次及以上取考核方式消考试资格。每次作业计100分，抄袭、给他人抄袭或未交作业不Measures得分，作业成绩为各次作业的平均分。平时成绩为出勤成绩×0.4+作业成绩×0.6。考核环节：环节负责人：期末 Final张永超，胡海娟DirectorAssessment Content给分形式课程总成绩比重(%):50百分制MarksResult TypePercentage (%)考核方式：满分100分，通过批阅期末考试试卷给出学生成绩。Measures七，改进机制ImprovementMechanism注：未尽事宜以教学团队以及学院教学指导委员会商定为准。10/11

10 / 11 注：可根据实际情况增减行数或修改内容 Note: Please add/reduce linesor revise content based on subject. 勾选 Check 教学方法与特色 Teaching Methodology & Characters  多媒体教学：基于信息化设备的课堂教学 Multi-media-basedlecturing  实践能力传授：理论与行业、实际案例相结合 Combining theory with industrial practical problems  课程思政建设：知识讲授与德育相结合 Knowledgedeliverywithethiceducation ☐ PBL 教学：问题驱动的分组学习与交流 Problem-basedlearning ☐ 其他:单击或点击此处输入文字。 Other:单击或点击此处输入文字。 六、成绩评定 Assessment 注：可根据实际情况增减行数或修改内容 Note: Please add/reduce linesor revise content based on subject. 考核环节: Assessment Content 平时 Behavior 环节负责人: Director 张永超，胡海娟 给分形式: Result Type 百分制 Marks 课程总成绩比重(%): Percentage (%) 50 考核方式: Measures 出勤 100 分，每次考勤计 10 分，缺勤不得分，缺勤五次及以上取 消考试资格。每次作业计 100 分，抄袭、给他人抄袭或未交作业不 得分，作业成绩为各次作业的平均分。平时成绩为出勤成绩0.4+ 作业成绩0.6。 考核环节: Assessment Content 期末 Final 环节负责人: Director 张永超，胡海娟 给分形式: Result Type 百分制 Marks 课程总成绩比重(%): Percentage (%) 50 考核方式: Measures 满分 100 分，通过批阅期末考试试卷给出学生成绩。 七、改进机制 Improvement Mechanism 注：未尽事宜以教学团队以及学院教学指导委员会商定为准