课程信息
4.3
51 个评分
21 个审阅
100% 在线

100% 在线

立即开始,按照自己的计划学习。
可灵活调整截止日期

可灵活调整截止日期

根据您的日程表重置截止日期。
中级

中级

完成时间(小时)

完成时间大约为32 小时

建议:8 weeks of study, 6-8 hours per week...
可选语言

英语(English)

字幕:英语(English)
100% 在线

100% 在线

立即开始,按照自己的计划学习。
可灵活调整截止日期

可灵活调整截止日期

根据您的日程表重置截止日期。
中级

中级

完成时间(小时)

完成时间大约为32 小时

建议:8 weeks of study, 6-8 hours per week...
可选语言

英语(English)

字幕:英语(English)

教学大纲 - 您将从这门课程中学到什么

1
完成时间(小时)
完成时间为 2 小时

Week 1: Introduction & Renewal processes

Upon completing this week, the learner will be able to understand the basic notions of probability theory, give a definition of a stochastic process; plot a trajectory and find finite-dimensional distributions for simple stochastic processes. Moreover, the learner will be able to apply Renewal Theory to marketing, both calculate the mathematical expectation of a countable process for any renewal process...
Reading
12 个视频 (总计 88 分钟), 1 个测验
Video12 个视频
Welcome1分钟
Week 1.1: Difference between deterministic and stochastic world4分钟
Week 1.2: Difference between various fields of stochastics6分钟
Week 1.3: Probability space8分钟
Week 1.4: Definition of a stochastic function. Types of stochastic functions.4分钟
Week 1.5: Trajectories and finite-dimensional distributions5分钟
Week 1.6: Renewal process. Counting process7分钟
Week 1.7: Convolution11分钟
Week 1.8: Laplace transform. Calculation of an expectation of a counting process-17分钟
Week 1.9: Laplace transform. Calculation of an expectation of a counting process-26分钟
Week 1.10: Laplace transform. Calculation of an expectation of a counting process-38分钟
Week 1.11: Limit theorems for renewal processes14分钟
Quiz1 个练习
Introduction & Renewal processes12分钟
2
完成时间(小时)
完成时间为 2 小时

Week 2: Poisson Processes

Upon completing this week, the learner will be able to understand the definitions and main properties of Poisson processes of different types and apply these processes to various real-life tasks, for instance, to model customer activity in marketing and to model aggregated claim sizes in insurance; understand a relation of this kind of models to Queueing Theory...
Reading
17 个视频 (总计 89 分钟), 1 个测验
Video17 个视频
Week 2.2: Definition of a Poisson process as a special example of renewal process. Exact forms of the distributions of the renewal process and the counting process-23分钟
Week 2.3: Definition of a Poisson process as a special example of renewal process. Exact forms of the distributions of the renewal process and the counting process-34分钟
Week 2.4: Definition of a Poisson process as a special example of renewal process. Exact forms of the distributions of the renewal process and the counting process-44分钟
Week 2.5: Memoryless property5分钟
Week 2.6: Other definitions of Poisson processes-13分钟
Week 2.7: Other definitions of Poisson processes-24分钟
Week 2.8: Non-homogeneous Poisson processes-14分钟
Week 2.9: Non-homogeneous Poisson processes-24分钟
Week 2.10: Relation between renewal theory and non-homogeneous Poisson processes-14分钟
Week 2.11: Relation between renewal theory and non-homogeneous Poisson processes-27分钟
Week 2.12: Relation between renewal theory and non-homogeneous Poisson processes-34分钟
Week 2.13: Elements of the queueing theory. M/G/k systems-19分钟
Week 2.14: Elements of the queueing theory. M/G/k systems-25分钟
Week 2.15: Compound Poisson processes-16分钟
Week 2.16: Compound Poisson processes-26分钟
Week 2.17: Compound Poisson processes-33分钟
Quiz1 个练习
Poisson processes & Queueing theory14分钟
3
完成时间(小时)
完成时间为 1 小时

Week 3: Markov Chains

Upon completing this week, the learner will be able to identify whether the process is a Markov chain and characterize it; classify the states of a Markov chain and apply ergodic theorem for finding limiting distributions on states...
Reading
7 个视频 (总计 73 分钟), 1 个测验
Video7 个视频
Week 3.2: Matrix representation of a Markov chain. Transition matrix. Chapman-Kolmogorov equation11分钟
Week 3.3: Graphic representation. Classification of states-110分钟
Week 3.4: Graphic representation. Classification of states-24分钟
Week 3.5: Graphic representation. Classification of states-37分钟
Week 3.6: Ergodic chains. Ergodic theorem-16分钟
Week 3.7: Ergodic chains. Ergodic theorem-215分钟
Quiz1 个练习
Markov Chains12分钟
4
完成时间(小时)
完成时间为 2 小时

Week 4: Gaussian Processes

Upon completing this week, the learner will be able to understand the notions of Gaussian vector, Gaussian process and Brownian motion (Wiener process); define a Gaussian process by its mean and covariance function and apply the theoretical properties of Brownian motion for solving various tasks...
Reading
8 个视频 (总计 87 分钟), 1 个测验
Video8 个视频
Week 4.2: Gaussian vector. Definition and main properties19分钟
Week 4.3: Connection between independence of normal random variables and absence of correlation13分钟
Week 4.4: Definition of a Gaussian process. Covariance function-15分钟
Week 4.5: Definition of a Gaussian process. Covariance function-210分钟
Week 4.6: Two definitions of a Brownian motion18分钟
Week 4.7: Modification of a process. Kolmogorov continuity theorem7分钟
Week 4.8: Main properties of Brownian motion6分钟
Quiz1 个练习
Gaussian processes12分钟

讲师

Avatar

Vladimir Panov

Assistant Professor
Faculty of economic sciences, HSE

关于 National Research University Higher School of Economics

National Research University - Higher School of Economics (HSE) is one of the top research universities in Russia. Established in 1992 to promote new research and teaching in economics and related disciplines, it now offers programs at all levels of university education across an extraordinary range of fields of study including business, sociology, cultural studies, philosophy, political science, international relations, law, Asian studies, media and communications, IT, mathematics, engineering, and more. Learn more on www.hse.ru...

常见问题

  • 注册以便获得证书后,您将有权访问所有视频、测验和编程作业(如果适用)。只有在您的班次开课之后,才可以提交和审阅同学互评作业。如果您选择在不购买的情况下浏览课程,可能无法访问某些作业。

  • 您购买证书后,将有权访问所有课程材料,包括评分作业。完成课程后,您的电子课程证书将添加到您的成就页中,您可以通过该页打印您的课程证书或将其添加到您的领英档案中。如果您只想阅读和查看课程内容,可以免费旁听课程。

还有其他问题吗?请访问 学生帮助中心