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。

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中級レベル

約28時間で修了

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

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

約28時間で修了

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

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...
12件のビデオ (合計88分), 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 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の練習問題
Poisson processes & Queueing theory14 分
3
1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...
7件のビデオ (合計73分), 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 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の練習問題
Gaussian processes12 分
5
2時間で修了

Week 5: Stationarity and Linear filters

Upon completing this week, the learner will be able to determine whether a given stochastic process is stationary and ergodic; determine whether a given stochastic process has a continuous modification; calculate the spectral density of a given wide-sense stationary process and apply spectral functions to the analysis of linear filters....
8件のビデオ (合計78分), 1 quiz
8件のビデオ
Week 5.2: Two types of stationarity-28 分
Week 5.3: Spectral density of a wide-sense stationary process-17 分
Week 5.4: Spectral density of a wide-sense stationary process-24 分
Week 5.5: Stochastic integration of the simplest type10 分
Week 5.6: Moving-average filters-15 分
Week 5.7: Moving-average filters-212 分
Week 5.8: Moving-average filters-38 分
1の練習問題
Stationarity and linear filters12 分
6
1時間で修了

Week 6: Ergodicity, differentiability, continuity

Upon completing this week, the learner will be able to determine whether a given stochastic process is differentiable and apply the term of continuity and ergodicity to stochastic processes...
4件のビデオ (合計53分), 1 quiz
4件のビデオ
Week 6.2: Ergodicity of wide-sense stationary processes15 分
Week 6.3: Definition of a stochastic derivative11 分
Week 6.4: Continuity in the mean-squared sense9 分
1の練習問題
Ergodicity, differentiability, continuity10 分
7
2時間で修了

Week 7: Stochastic integration & Itô formula

Upon completing this week, the learner will be able to calculate stochastic integrals of various types and apply Itô’s formula for calculation of stochastic integrals as well as for construction of various stochastic models....
10件のビデオ (合計82分), 1 quiz
10件のビデオ
Week 7.2: Integrals of the type ∫ f(t) dW_t-113 分
Week 7.3: Integrals of the type ∫ f(t) dW_t-211 分
Week 7.4: Integrals of the type ∫ X_t dW_t-15 分
Week 7.5: Integrals of the type ∫ X_t dW_t-214 分
Week 7.6: Integrals of the type ∫ X_t dY_t, where Y_t is an Itô process6 分
Week 7.7: Itô’s formula8 分
Week 7.8: Calculation of stochastic integrals using the Itô formula. Black-Scholes model6 分
Week 7.9: Vasicek model. Application of the Itô formula to stochastic modelling5 分
Week 7.10: Ornstein-Uhlenbeck process. Application of the Itô formula to stochastic modelling.4 分
1の練習問題
Stochastic integration12 分
8
2時間で修了

Week 8: Lévy processes

Upon completing this week, the learner will be able to understand the main properties of Lévy processes; construct a Lévy process from an infinitely-divisible distribution; characterize the activity of jumps of a given Lévy process; apply the Lévy-Khintchine representation for a particular Lévy process and understand the time change techniques, stochastic volatility approach are other ideas for construction of Lévy-based models....
10件のビデオ (合計94分), 1 quiz
10件のビデオ
Week 8.2: Examples of Lévy processes. Calculation of the characteristic function in particular cases17 分
Week 8.3: Relation to the infinitely divisible distributions7 分
Week 8.4: Characteristic exponent8 分
Week 8.5: Properties of a Lévy process, which directly follow from the existence of characteristic exponent7 分
Week 8.6: Lévy-Khintchine representation and Lévy-Khintchine triplet-17 分
Week 8.7: Lévy-Khintchine representation and Lévy-Khintchine triplet-27 分
Week 8.8: Lévy-Khintchine representation and Lévy-Khintchine triplet-38 分
Week 8.9: Modelling of jump-type dynamics. Lévy-based models7 分
Week 8.10: Time-changed stochastic processes. Monroe theorem9 分
1の練習問題
Lévy processes12 分
9
16分で修了

Final exam

This module includes final exam covering all topics of this course...
1 quiz
1の練習問題
Final Exam16 分
4.4
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人気のレビュー

by ZMDec 1st 2018

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

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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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