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Start instantly and learn at your own schedule.

#### Approx. 28 hours to complete

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

#### English

Subtitles: English

## 60%

got a tangible career benefit from this course

## 14%

got a pay increase or promotion

#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 28 hours to complete

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

#### English

Subtitles: English

# Syllabus - What you will learn from this course

Week
1

## Week 1

2 hours to complete

# Week 1: Introduction & Renewal processes

2 hours to complete
12 videos (Total 88 min), 1 reading, 1 quiz
12 videos
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
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 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 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 practice exercise
Gaussian processes12m
4.5

# 48 Reviews

### Top reviews from Stochastic processes

By CRSep 14th 2019

This was helpful but I still feel I don't understand stochastic processes. Folks taking this course should know that it's pretty tough, compared to most Coursera courses.

By MMSep 23rd 2019

Great course! The subject material was well covered and it gave me the tools to tackle more advanced stochastic, like population dynamics or quantitative finance.

### Instructor

Assistant Professor
Faculty of economic sciences, HSE

### About 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 communicamathematics, engineering, and more. Learn more on www.hse.ru...