このコースについて
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#### 柔軟性のある期限

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#### 柔軟性のある期限

スケジュールに従って期限をリセットします。

1
2時間で修了

## Week 1: Introduction & Renewal processes

12件のビデオ （合計88分）, 1 reading, 1 quiz
12件のビデオ
Welcome1 分
Week 1.1: Difference between deterministic and stochastic world4 分
Week 1.2: Difference between various fields of stochastics6 分
Week 1.3: Probability space8 分
Week 1.4: Definition of a stochastic function. Types of stochastic functions.4 分
Week 1.5: Trajectories and finite-dimensional distributions5 分
Week 1.6: Renewal process. Counting process7 分
Week 1.7: Convolution11 分
Week 1.8: Laplace transform. Calculation of an expectation of a counting process-17 分
Week 1.9: Laplace transform. Calculation of an expectation of a counting process-26 分
Week 1.10: Laplace transform. Calculation of an expectation of a counting process-38 分
Week 1.11: Limit theorems for renewal processes14 分
1件の学習用教材
1の練習問題
Introduction & Renewal processes12 分
2
2時間で修了

## Week 2: Poisson Processes

17件のビデオ （合計89分）, 1 reading, 1 quiz
17件のビデオ
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
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
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
Week 2.5: Memoryless property5 分
Week 2.6: Other definitions of Poisson processes-13 分
Week 2.7: Other definitions of Poisson processes-24 分
Week 2.8: Non-homogeneous Poisson processes-14 分
Week 2.9: Non-homogeneous Poisson processes-24 分
Week 2.10: Relation between renewal theory and non-homogeneous Poisson processes-14 分
Week 2.11: Relation between renewal theory and non-homogeneous Poisson processes-27 分
Week 2.12: Relation between renewal theory and non-homogeneous Poisson processes-34 分
Week 2.13: Elements of the queueing theory. M/G/k systems-19 分
Week 2.14: Elements of the queueing theory. M/G/k systems-25 分
Week 2.15: Compound Poisson processes-16 分
Week 2.16: Compound Poisson processes-26 分
Week 2.17: Compound Poisson processes-33 分
1件の学習用教材
1の練習問題
Poisson processes & Queueing theory14 分
3
2時間で修了

## Week 3: Markov Chains

7件のビデオ （合計73分）, 1 reading, 1 quiz
7件のビデオ
Week 3.2: Matrix representation of a Markov chain. Transition matrix. Chapman-Kolmogorov equation11 分
Week 3.3: Graphic representation. Classification of states-110 分
Week 3.4: Graphic representation. Classification of states-24 分
Week 3.5: Graphic representation. Classification of states-37 分
Week 3.6: Ergodic chains. Ergodic theorem-16 分
Week 3.7: Ergodic chains. Ergodic theorem-215 分
1件の学習用教材
1の練習問題
Markov Chains12 分
4
2時間で修了

## Week 4: Gaussian Processes

8件のビデオ （合計87分）, 1 reading, 1 quiz
8件のビデオ
Week 4.2: Gaussian vector. Definition and main properties19 分
Week 4.3: Connection between independence of normal random variables and absence of correlation13 分
Week 4.4: Definition of a Gaussian process. Covariance function-15 分
Week 4.5: Definition of a Gaussian process. Covariance function-210 分
Week 4.6: Two definitions of a Brownian motion18 分
Week 4.7: Modification of a process. Kolmogorov continuity theorem7 分
Week 4.8: Main properties of Brownian motion6 分
1件の学習用教材
1の練習問題
Gaussian processes12 分
4.5
45件のレビュー

## 60%

コースが具体的なキャリアアップにつながった

## 14%

### 確率過程 からの人気レビュー

by 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.

by 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

Assistant Professor
Faculty of economic sciences, HSE

## ロシア国立研究大学経済高等学院（National Research University Higher School of Economics）について

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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