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1

## Week 1: Introduction & Renewal processes

13 个视频 （总计 89 分钟）, 3 个阅读材料, 1 个测验
13 个视频
Welcome1分钟
Week 1.1: Difference between deterministic and stochastic world4分钟
Week 1.2: Difference between various fields of stochastics6分钟
Week 1.3: Probability space8分钟
Week 1.4: Definition of a stochastic function. Types of stochastic functions.4分钟
Week 1.5: Trajectories and finite-dimensional distributions5分钟
Week 1.6: Renewal process. Counting process7分钟
Week 1.7: Convolution11分钟
Week 1.8: Laplace transform. Calculation of an expectation of a counting process-17分钟
Week 1.9: Laplace transform. Calculation of an expectation of a counting process-26分钟
Week 1.10: Laplace transform. Calculation of an expectation of a counting process-38分钟
Week 1.11: Limit theorems for renewal processes14分钟
3 个阅读材料
Rules on the academic integrity in the course10分钟
1 个练习
Introduction & Renewal processes30分钟
2

## Week 2: Poisson Processes

17 个视频 （总计 89 分钟）, 1 个阅读材料, 1 个测验
17 个视频
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分钟
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分钟
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分钟
Week 2.5: Memoryless property5分钟
Week 2.6: Other definitions of Poisson processes-13分钟
Week 2.7: Other definitions of Poisson processes-24分钟
Week 2.8: Non-homogeneous Poisson processes-14分钟
Week 2.9: Non-homogeneous Poisson processes-24分钟
Week 2.10: Relation between renewal theory and non-homogeneous Poisson processes-14分钟
Week 2.11: Relation between renewal theory and non-homogeneous Poisson processes-27分钟
Week 2.12: Relation between renewal theory and non-homogeneous Poisson processes-34分钟
Week 2.13: Elements of the queueing theory. M/G/k systems-19分钟
Week 2.14: Elements of the queueing theory. M/G/k systems-25分钟
Week 2.15: Compound Poisson processes-16分钟
Week 2.16: Compound Poisson processes-26分钟
Week 2.17: Compound Poisson processes-33分钟
1 个阅读材料
1 个练习
Poisson processes & Queueing theory14分钟
3

## Week 3: Markov Chains

7 个视频 （总计 73 分钟）, 2 个阅读材料, 1 个测验
7 个视频
Week 3.2: Matrix representation of a Markov chain. Transition matrix. Chapman-Kolmogorov equation11分钟
Week 3.3: Graphic representation. Classification of states-110分钟
Week 3.4: Graphic representation. Classification of states-24分钟
Week 3.5: Graphic representation. Classification of states-37分钟
Week 3.6: Ergodic chains. Ergodic theorem-16分钟
Week 3.7: Ergodic chains. Ergodic theorem-215分钟
2 个阅读材料
Applications of the Markov chains10分钟
1 个练习
Markov Chains12分钟
4

## Week 4: Gaussian Processes

8 个视频 （总计 87 分钟）, 1 个阅读材料, 1 个测验
8 个视频
Week 4.2: Gaussian vector. Definition and main properties19分钟
Week 4.3: Connection between independence of normal random variables and absence of correlation13分钟
Week 4.4: Definition of a Gaussian process. Covariance function-15分钟
Week 4.5: Definition of a Gaussian process. Covariance function-210分钟
Week 4.6: Two definitions of a Brownian motion18分钟
Week 4.7: Modification of a process. Kolmogorov continuity theorem7分钟
Week 4.8: Main properties of Brownian motion6分钟
1 个阅读材料