Об этом курсе
4.3
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Прибл. 31 часа на выполнение

Предполагаемая нагрузка: 8 weeks of study, 6-8 hours per week...
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Английский

Субтитры: Английский
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Назначьте сроки сдачи в соответствии со своим графиком.
Промежуточный уровень

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Часов на завершение

Прибл. 31 часа на выполнение

Предполагаемая нагрузка: 8 weeks of study, 6-8 hours per week...
Доступные языки

Английский

Субтитры: Английский

Программа курса: что вы изучите

Неделя
1
Часов на завершение
2 ч. на завершение

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 videos (Total 88 min), 1 тест
Video12 видео
Welcome1мин
Week 1.1: Difference between deterministic and stochastic world4мин
Week 1.2: Difference between various fields of stochastics6мин
Week 1.3: Probability space8мин
Week 1.4: Definition of a stochastic function. Types of stochastic functions.4мин
Week 1.5: Trajectories and finite-dimensional distributions5мин
Week 1.6: Renewal process. Counting process7мин
Week 1.7: Convolution11мин
Week 1.8: Laplace transform. Calculation of an expectation of a counting process-17мин
Week 1.9: Laplace transform. Calculation of an expectation of a counting process-26мин
Week 1.10: Laplace transform. Calculation of an expectation of a counting process-38мин
Week 1.11: Limit theorems for renewal processes14мин
Quiz1 практическое упражнение
Introduction & Renewal processes12мин
Неделя
2
Часов на завершение
2 ч. на завершение

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 videos (Total 89 min), 1 тест
Video17 видео
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-23мин
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-34мин
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-44мин
Week 2.5: Memoryless property5мин
Week 2.6: Other definitions of Poisson processes-13мин
Week 2.7: Other definitions of Poisson processes-24мин
Week 2.8: Non-homogeneous Poisson processes-14мин
Week 2.9: Non-homogeneous Poisson processes-24мин
Week 2.10: Relation between renewal theory and non-homogeneous Poisson processes-14мин
Week 2.11: Relation between renewal theory and non-homogeneous Poisson processes-27мин
Week 2.12: Relation between renewal theory and non-homogeneous Poisson processes-34мин
Week 2.13: Elements of the queueing theory. M/G/k systems-19мин
Week 2.14: Elements of the queueing theory. M/G/k systems-25мин
Week 2.15: Compound Poisson processes-16мин
Week 2.16: Compound Poisson processes-26мин
Week 2.17: Compound Poisson processes-33мин
Quiz1 практическое упражнение
Poisson processes & Queueing theory14мин
Неделя
3
Часов на завершение
1 ч. на завершение

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 videos (Total 73 min), 1 тест
Video7 видео
Week 3.2: Matrix representation of a Markov chain. Transition matrix. Chapman-Kolmogorov equation11мин
Week 3.3: Graphic representation. Classification of states-110мин
Week 3.4: Graphic representation. Classification of states-24мин
Week 3.5: Graphic representation. Classification of states-37мин
Week 3.6: Ergodic chains. Ergodic theorem-16мин
Week 3.7: Ergodic chains. Ergodic theorem-215мин
Quiz1 практическое упражнение
Markov Chains12мин
Неделя
4
Часов на завершение
2 ч. на завершение

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 videos (Total 87 min), 1 тест
Video8 видео
Week 4.2: Gaussian vector. Definition and main properties19мин
Week 4.3: Connection between independence of normal random variables and absence of correlation13мин
Week 4.4: Definition of a Gaussian process. Covariance function-15мин
Week 4.5: Definition of a Gaussian process. Covariance function-210мин
Week 4.6: Two definitions of a Brownian motion18мин
Week 4.7: Modification of a process. Kolmogorov continuity theorem7мин
Week 4.8: Main properties of Brownian motion6мин
Quiz1 практическое упражнение
Gaussian processes12мин

Преподаватель

Avatar

Vladimir Panov

Assistant Professor
Faculty of economic sciences, HSE

О 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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