このコースについて
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自分のスケジュールですぐに学習を始めてください。

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。

中級レベル

英語

字幕:英語

100%オンライン

自分のスケジュールですぐに学習を始めてください。

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。

中級レベル

英語

字幕:英語

シラバス - 本コースの学習内容

1
2時間で修了

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

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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
Quiz-1 answers and solutions10 分
1の練習問題
Introduction & Renewal processes12 分
2
2時間で修了

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

...
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
Quiz-2 answers and solutions10 分
1の練習問題
Poisson processes & Queueing theory14 分
3
2時間で修了

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

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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
Quiz-3 answers and solutions10 分
1の練習問題
Markov Chains12 分
4
2時間で修了

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

...
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
Quiz-4 answers and solutions10 分
1の練習問題
Gaussian processes12 分
4.4
33件のレビューChevron Right

43%

コースが具体的なキャリアアップにつながった

確率過程 からの人気レビュー

by SSMay 21st 2019

This course has less number of quiz questions but sufficient and well designed questions.

by ZMDec 1st 2018

Well presented course. I enjoyed it and was challenged a great deal. Thank you.

講師

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Vladimir Panov

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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