Об этом курсе
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Предполагаемая нагрузка: 8 weeks of study, 6-8 hours per week...

Английский

Субтитры: Английский

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Прибл. 28 часа на выполнение

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

Английский

Субтитры: Английский

Программа курса: что вы изучите

Неделя
1
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

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12 видео ((всего 88 мин.)), 1 материал для самостоятельного изучения, 1 тест
12 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
1 материал для самостоятельного изучения
Quiz-1 answers and solutions10мин
1 практическое упражнение
Introduction & Renewal processes12мин
Неделя
2
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

...
17 видео ((всего 89 мин.)), 1 материал для самостоятельного изучения, 1 тест
17 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
1 материал для самостоятельного изучения
Quiz-2 answers and solutions10мин
1 практическое упражнение
Poisson processes & Queueing theory14мин
Неделя
3
2 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

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7 видео ((всего 73 мин.)), 1 материал для самостоятельного изучения, 1 тест
7 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
1 материал для самостоятельного изучения
Quiz-3 answers and solutions10мин
1 практическое упражнение
Markov Chains12мин
Неделя
4
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

...
8 видео ((всего 87 мин.)), 1 материал для самостоятельного изучения, 1 тест
8 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
1 материал для самостоятельного изучения
Quiz-4 answers and solutions10мин
1 практическое упражнение
Gaussian processes12мин
Неделя
5
2 ч. на завершение

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.

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8 видео ((всего 78 мин.)), 1 материал для самостоятельного изучения, 1 тест
8 видео
Week 5.2: Two types of stationarity-28мин
Week 5.3: Spectral density of a wide-sense stationary process-17мин
Week 5.4: Spectral density of a wide-sense stationary process-24мин
Week 5.5: Stochastic integration of the simplest type10мин
Week 5.6: Moving-average filters-15мин
Week 5.7: Moving-average filters-212мин
Week 5.8: Moving-average filters-38мин
1 материал для самостоятельного изучения
Quiz-5 answers and solutions10мин
1 практическое упражнение
Stationarity and linear filters12мин
Неделя
6
1 ч. на завершение

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

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4 видео ((всего 53 мин.)), 1 материал для самостоятельного изучения, 1 тест
4 видео
Week 6.2: Ergodicity of wide-sense stationary processes15мин
Week 6.3: Definition of a stochastic derivative11мин
Week 6.4: Continuity in the mean-squared sense9мин
1 материал для самостоятельного изучения
Quiz-6 answers and solutions10мин
1 практическое упражнение
Ergodicity, differentiability, continuity10мин
Неделя
7
2 ч. на завершение

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.

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10 видео ((всего 82 мин.)), 1 тест
10 видео
Week 7.2: Integrals of the type ∫ f(t) dW_t-113мин
Week 7.3: Integrals of the type ∫ f(t) dW_t-211мин
Week 7.4: Integrals of the type ∫ X_t dW_t-15мин
Week 7.5: Integrals of the type ∫ X_t dW_t-214мин
Week 7.6: Integrals of the type ∫ X_t dY_t, where Y_t is an Itô process6мин
Week 7.7: Itô’s formula8мин
Week 7.8: Calculation of stochastic integrals using the Itô formula. Black-Scholes model6мин
Week 7.9: Vasicek model. Application of the Itô formula to stochastic modelling5мин
Week 7.10: Ornstein-Uhlenbeck process. Application of the Itô formula to stochastic modelling.4мин
1 практическое упражнение
Stochastic integration12мин
Неделя
8
2 ч. на завершение

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 видео ((всего 94 мин.)), 1 тест
10 видео
Week 8.2: Examples of Lévy processes. Calculation of the characteristic function in particular cases17мин
Week 8.3: Relation to the infinitely divisible distributions7мин
Week 8.4: Characteristic exponent8мин
Week 8.5: Properties of a Lévy process, which directly follow from the existence of characteristic exponent7мин
Week 8.6: Lévy-Khintchine representation and Lévy-Khintchine triplet-17мин
Week 8.7: Lévy-Khintchine representation and Lévy-Khintchine triplet-27мин
Week 8.8: Lévy-Khintchine representation and Lévy-Khintchine triplet-38мин
Week 8.9: Modelling of jump-type dynamics. Lévy-based models7мин
Week 8.10: Time-changed stochastic processes. Monroe theorem9мин
1 практическое упражнение
Lévy processes12мин
Неделя
9
16 минуты на завершение

Final exam

This module includes final exam covering all topics of this course

...
1 тест
1 практическое упражнение
Final Exam16мин
4.4
Рецензии: 33Chevron Right

43%

получил значимые преимущества в карьере благодаря этому курсу

Лучшие отзывы о курсе Стохастический процесс

автор: SSMay 21st 2019

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

автор: ZMDec 1st 2018

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

Преподаватели

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Vladimir Panov

Assistant Professor
Faculty of economic sciences, HSE

О Национальный исследовательский университет "Высшая школа экономики"

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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