4.3
49 個評分
20 個審閱

1

## 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 個視頻 （總計 88 分鐘）, 1 個測驗
12 個視頻
Welcome1分鐘
Week 1.1: Difference between deterministic and stochastic world4分鐘
Week 1.2: Difference between various fields of stochastics6分鐘
Week 1.3: Probability space8分鐘
Week 1.4: Definition of a stochastic function. Types of stochastic functions.4分鐘
Week 1.5: Trajectories and finite-dimensional distributions5分鐘
Week 1.6: Renewal process. Counting process7分鐘
Week 1.7: Convolution11分鐘
Week 1.8: Laplace transform. Calculation of an expectation of a counting process-17分鐘
Week 1.9: Laplace transform. Calculation of an expectation of a counting process-26分鐘
Week 1.10: Laplace transform. Calculation of an expectation of a counting process-38分鐘
Week 1.11: Limit theorems for renewal processes14分鐘
1 個練習
Introduction & Renewal processes12分鐘
2

## 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 個視頻 （總計 89 分鐘）, 1 個測驗
17 個視頻
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分鐘
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分鐘
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分鐘
Week 2.5: Memoryless property5分鐘
Week 2.6: Other definitions of Poisson processes-13分鐘
Week 2.7: Other definitions of Poisson processes-24分鐘
Week 2.8: Non-homogeneous Poisson processes-14分鐘
Week 2.9: Non-homogeneous Poisson processes-24分鐘
Week 2.10: Relation between renewal theory and non-homogeneous Poisson processes-14分鐘
Week 2.11: Relation between renewal theory and non-homogeneous Poisson processes-27分鐘
Week 2.12: Relation between renewal theory and non-homogeneous Poisson processes-34分鐘
Week 2.13: Elements of the queueing theory. M/G/k systems-19分鐘
Week 2.14: Elements of the queueing theory. M/G/k systems-25分鐘
Week 2.15: Compound Poisson processes-16分鐘
Week 2.16: Compound Poisson processes-26分鐘
Week 2.17: Compound Poisson processes-33分鐘
1 個練習
Poisson processes & Queueing theory14分鐘
3

## 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 個視頻 （總計 73 分鐘）, 1 個測驗
7 個視頻
Week 3.2: Matrix representation of a Markov chain. Transition matrix. Chapman-Kolmogorov equation11分鐘
Week 3.3: Graphic representation. Classification of states-110分鐘
Week 3.4: Graphic representation. Classification of states-24分鐘
Week 3.5: Graphic representation. Classification of states-37分鐘
Week 3.6: Ergodic chains. Ergodic theorem-16分鐘
Week 3.7: Ergodic chains. Ergodic theorem-215分鐘
1 個練習
Markov Chains12分鐘
4

## 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 個視頻 （總計 87 分鐘）, 1 個測驗
8 個視頻
Week 4.2: Gaussian vector. Definition and main properties19分鐘
Week 4.3: Connection between independence of normal random variables and absence of correlation13分鐘
Week 4.4: Definition of a Gaussian process. Covariance function-15分鐘
Week 4.5: Definition of a Gaussian process. Covariance function-210分鐘
Week 4.6: Two definitions of a Brownian motion18分鐘
Week 4.7: Modification of a process. Kolmogorov continuity theorem7分鐘
Week 4.8: Main properties of Brownian motion6分鐘
1 個練習
Gaussian processes12分鐘

## 講師

Assistant Professor
Faculty of economic sciences, HSE

## 關於 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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