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中級

完成時間大約為29 小時

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

英語(English)

字幕:英語(English)

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

根據您的日程表重置截止日期。

中級

完成時間大約為29 小時

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

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
完成時間為 2 小時

Week 1: Introduction & Renewal processes

12 個視頻 (總計 88 分鐘), 1 個閱讀材料, 1 個測驗
12 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
1 個閱讀材料
Quiz-1 answers and solutions10分鐘
1 個練習
Introduction & Renewal processes12分鐘
2
完成時間為 2 小時

Week 2: Poisson Processes

17 個視頻 (總計 89 分鐘), 1 個閱讀材料, 1 個測驗
17 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
1 個閱讀材料
Quiz-2 answers and solutions10分鐘
1 個練習
Poisson processes & Queueing theory14分鐘
3
完成時間為 2 小時

Week 3: Markov Chains

7 個視頻 (總計 73 分鐘), 1 個閱讀材料, 1 個測驗
7 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
1 個閱讀材料
Quiz-3 answers and solutions10分鐘
1 個練習
Markov Chains12分鐘
4
完成時間為 2 小時

Week 4: Gaussian Processes

8 個視頻 (總計 87 分鐘), 1 個閱讀材料, 1 個測驗
8 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
1 個閱讀材料
Quiz-4 answers and solutions10分鐘
1 個練習
Gaussian processes12分鐘
4.4
42 個審閱Chevron Right

60%

通過此課程獲得實實在在的工作福利

14%

加薪或升職

來自随机过程的熱門評論

創建者 CRSep 14th 2019

This was helpful but I still feel I don't understand stochastic processes. Folks taking this course should know that it's pretty tough, compared to most Coursera courses.

創建者 MMSep 23rd 2019

Great course! The subject material was well covered and it gave me the tools to tackle more advanced stochastic, like population dynamics or quantitative finance.

講師

Avatar

Vladimir Panov

Assistant Professor
Faculty of economic sciences, HSE

關於 国立高等经济大学

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 communicamathematics, engineering, and more. Learn more on www.hse.ru...

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