About this Course

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Learner Career Outcomes

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Shareable Certificate
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100% online
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Flexible deadlines
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Intermediate Level
Approx. 15 hours to complete
English
Subtitles: English

Learner Career Outcomes

60%

got a tangible career benefit from this course

14%

got a pay increase or promotion
Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Flexible deadlines
Reset deadlines in accordance to your schedule.
Intermediate Level
Approx. 15 hours to complete
English
Subtitles: English

Offered by

National Research University Higher School of Economics logo

National Research University Higher School of Economics

Syllabus - What you will learn from this course

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Week
1

Week 1

2 hours to complete

Week 1: Introduction & Renewal processes

2 hours to complete
13 videos (Total 89 min), 2 readings, 1 quiz
13 videos
Welcome1m
Week 1.1: Difference between deterministic and stochastic world4m
Week 1.2: Difference between various fields of stochastics6m
Week 1.3: Probability space8m
Week 1.4: Definition of a stochastic function. Types of stochastic functions.4m
Week 1.5: Trajectories and finite-dimensional distributions5m
Week 1.6: Renewal process. Counting process7m
Week 1.7: Convolution11m
Week 1.8: Laplace transform. Calculation of an expectation of a counting process-17m
Week 1.9: Laplace transform. Calculation of an expectation of a counting process-26m
Week 1.10: Laplace transform. Calculation of an expectation of a counting process-38m
Week 1.11: Limit theorems for renewal processes14m
2 readings
About the University10m
Quiz-1 answers and solutions10m
1 practice exercise
Introduction & Renewal processes12m
Week
2

Week 2

2 hours to complete

Week 2: Poisson Processes

2 hours to complete
17 videos (Total 89 min), 1 reading, 1 quiz
17 videos
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-23m
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-34m
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-44m
Week 2.5: Memoryless property5m
Week 2.6: Other definitions of Poisson processes-13m
Week 2.7: Other definitions of Poisson processes-24m
Week 2.8: Non-homogeneous Poisson processes-14m
Week 2.9: Non-homogeneous Poisson processes-24m
Week 2.10: Relation between renewal theory and non-homogeneous Poisson processes-14m
Week 2.11: Relation between renewal theory and non-homogeneous Poisson processes-27m
Week 2.12: Relation between renewal theory and non-homogeneous Poisson processes-34m
Week 2.13: Elements of the queueing theory. M/G/k systems-19m
Week 2.14: Elements of the queueing theory. M/G/k systems-25m
Week 2.15: Compound Poisson processes-16m
Week 2.16: Compound Poisson processes-26m
Week 2.17: Compound Poisson processes-33m
1 reading
Quiz-2 answers and solutions10m
1 practice exercise
Poisson processes & Queueing theory14m
Week
3

Week 3

2 hours to complete

Week 3: Markov Chains

2 hours to complete
7 videos (Total 73 min), 1 reading, 1 quiz
7 videos
Week 3.2: Matrix representation of a Markov chain. Transition matrix. Chapman-Kolmogorov equation11m
Week 3.3: Graphic representation. Classification of states-110m
Week 3.4: Graphic representation. Classification of states-24m
Week 3.5: Graphic representation. Classification of states-37m
Week 3.6: Ergodic chains. Ergodic theorem-16m
Week 3.7: Ergodic chains. Ergodic theorem-215m
1 reading
Quiz-3 answers and solutions10m
1 practice exercise
Markov Chains12m
Week
4

Week 4

2 hours to complete

Week 4: Gaussian Processes

2 hours to complete
8 videos (Total 87 min), 1 reading, 1 quiz
8 videos
Week 4.2: Gaussian vector. Definition and main properties19m
Week 4.3: Connection between independence of normal random variables and absence of correlation13m
Week 4.4: Definition of a Gaussian process. Covariance function-15m
Week 4.5: Definition of a Gaussian process. Covariance function-210m
Week 4.6: Two definitions of a Brownian motion18m
Week 4.7: Modification of a process. Kolmogorov continuity theorem7m
Week 4.8: Main properties of Brownian motion6m
1 reading
Quiz-4 answers and solutions10m
1 practice exercise
Gaussian processes12m

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