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## Week 1: Introduction & Renewal processes

13 個視頻 （總計 89 分鐘）, 2 個閱讀材料, 1 個測驗
13 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
2 個閱讀材料
1 個練習
Introduction & Renewal processes12分鐘
2

## Week 2: Poisson Processes

17 個視頻 （總計 89 分鐘）, 1 個閱讀材料, 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 個閱讀材料
1 個練習
Poisson processes & Queueing theory14分鐘
3

## Week 3: Markov Chains

7 個視頻 （總計 73 分鐘）, 1 個閱讀材料, 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 個閱讀材料
1 個練習
Markov Chains12分鐘
4

## Week 4: Gaussian Processes

8 個視頻 （總計 87 分鐘）, 1 個閱讀材料, 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 個閱讀材料
1 個練習
Gaussian processes12分鐘

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