課程信息
4.3
49 個評分
20 個審閱
100% 在線

100% 在線

立即開始,按照自己的計劃學習。
可靈活調整截止日期

可靈活調整截止日期

根據您的日程表重置截止日期。
中級

中級

完成時間(小時)

完成時間大約為31 小時

建議:8 weeks of study, 6-8 hours per week...
可選語言

英語(English)

字幕:英語(English)
100% 在線

100% 在線

立即開始,按照自己的計劃學習。
可靈活調整截止日期

可靈活調整截止日期

根據您的日程表重置截止日期。
中級

中級

完成時間(小時)

完成時間大約為31 小時

建議:8 weeks of study, 6-8 hours per week...
可選語言

英語(English)

字幕:英語(English)

教學大綱 - 您將從這門課程中學到什麼

1
完成時間(小時)
完成時間為 2 小時

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 個視頻 (總計 88 分鐘), 1 個測驗
Video12 個視頻
Welcome1分鐘
Week 1.1: Difference between deterministic and stochastic world4分鐘
Week 1.2: Difference between various fields of stochastics6分鐘
Week 1.3: Probability space8分鐘
Week 1.4: Definition of a stochastic function. Types of stochastic functions.4分鐘
Week 1.5: Trajectories and finite-dimensional distributions5分鐘
Week 1.6: Renewal process. Counting process7分鐘
Week 1.7: Convolution11分鐘
Week 1.8: Laplace transform. Calculation of an expectation of a counting process-17分鐘
Week 1.9: Laplace transform. Calculation of an expectation of a counting process-26分鐘
Week 1.10: Laplace transform. Calculation of an expectation of a counting process-38分鐘
Week 1.11: Limit theorems for renewal processes14分鐘
Quiz1 個練習
Introduction & Renewal processes12分鐘
2
完成時間(小時)
完成時間為 2 小時

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 個視頻 (總計 89 分鐘), 1 個測驗
Video17 個視頻
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分鐘
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分鐘
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分鐘
Week 2.5: Memoryless property5分鐘
Week 2.6: Other definitions of Poisson processes-13分鐘
Week 2.7: Other definitions of Poisson processes-24分鐘
Week 2.8: Non-homogeneous Poisson processes-14分鐘
Week 2.9: Non-homogeneous Poisson processes-24分鐘
Week 2.10: Relation between renewal theory and non-homogeneous Poisson processes-14分鐘
Week 2.11: Relation between renewal theory and non-homogeneous Poisson processes-27分鐘
Week 2.12: Relation between renewal theory and non-homogeneous Poisson processes-34分鐘
Week 2.13: Elements of the queueing theory. M/G/k systems-19分鐘
Week 2.14: Elements of the queueing theory. M/G/k systems-25分鐘
Week 2.15: Compound Poisson processes-16分鐘
Week 2.16: Compound Poisson processes-26分鐘
Week 2.17: Compound Poisson processes-33分鐘
Quiz1 個練習
Poisson processes & Queueing theory14分鐘
3
完成時間(小時)
完成時間為 1 小時

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 個視頻 (總計 73 分鐘), 1 個測驗
Video7 個視頻
Week 3.2: Matrix representation of a Markov chain. Transition matrix. Chapman-Kolmogorov equation11分鐘
Week 3.3: Graphic representation. Classification of states-110分鐘
Week 3.4: Graphic representation. Classification of states-24分鐘
Week 3.5: Graphic representation. Classification of states-37分鐘
Week 3.6: Ergodic chains. Ergodic theorem-16分鐘
Week 3.7: Ergodic chains. Ergodic theorem-215分鐘
Quiz1 個練習
Markov Chains12分鐘
4
完成時間(小時)
完成時間為 2 小時

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 個視頻 (總計 87 分鐘), 1 個測驗
Video8 個視頻
Week 4.2: Gaussian vector. Definition and main properties19分鐘
Week 4.3: Connection between independence of normal random variables and absence of correlation13分鐘
Week 4.4: Definition of a Gaussian process. Covariance function-15分鐘
Week 4.5: Definition of a Gaussian process. Covariance function-210分鐘
Week 4.6: Two definitions of a Brownian motion18分鐘
Week 4.7: Modification of a process. Kolmogorov continuity theorem7分鐘
Week 4.8: Main properties of Brownian motion6分鐘
Quiz1 個練習
Gaussian processes12分鐘

講師

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Vladimir Panov

Assistant Professor
Faculty of economic sciences, HSE

關於 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...

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