About this Course
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Intermediate Level

Approx. 28 hours to complete

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

English

Subtitles: English

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Intermediate Level

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
2 hours to complete

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 videos (Total 88 min), 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
2 hours to complete

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 videos (Total 89 min), 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
1 hour to complete

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 videos (Total 73 min), 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
2 hours to complete

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 videos (Total 87 min), 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
Week
5
2 hours to complete

Week 5: Stationarity and Linear filters

Upon completing this week, the learner will be able to determine whether a given stochastic process is stationary and ergodic; determine whether a given stochastic process has a continuous modification; calculate the spectral density of a given wide-sense stationary process and apply spectral functions to the analysis of linear filters....
8 videos (Total 78 min), 1 quiz
8 videos
Week 5.2: Two types of stationarity-28m
Week 5.3: Spectral density of a wide-sense stationary process-17m
Week 5.4: Spectral density of a wide-sense stationary process-24m
Week 5.5: Stochastic integration of the simplest type10m
Week 5.6: Moving-average filters-15m
Week 5.7: Moving-average filters-212m
Week 5.8: Moving-average filters-38m
1 practice exercise
Stationarity and linear filters12m
Week
6
1 hour to complete

Week 6: Ergodicity, differentiability, continuity

Upon completing this week, the learner will be able to determine whether a given stochastic process is differentiable and apply the term of continuity and ergodicity to stochastic processes...
4 videos (Total 53 min), 1 quiz
4 videos
Week 6.2: Ergodicity of wide-sense stationary processes15m
Week 6.3: Definition of a stochastic derivative11m
Week 6.4: Continuity in the mean-squared sense9m
1 practice exercise
Ergodicity, differentiability, continuity10m
Week
7
2 hours to complete

Week 7: Stochastic integration & Itô formula

Upon completing this week, the learner will be able to calculate stochastic integrals of various types and apply Itô’s formula for calculation of stochastic integrals as well as for construction of various stochastic models....
10 videos (Total 82 min), 1 quiz
10 videos
Week 7.2: Integrals of the type ∫ f(t) dW_t-113m
Week 7.3: Integrals of the type ∫ f(t) dW_t-211m
Week 7.4: Integrals of the type ∫ X_t dW_t-15m
Week 7.5: Integrals of the type ∫ X_t dW_t-214m
Week 7.6: Integrals of the type ∫ X_t dY_t, where Y_t is an Itô process6m
Week 7.7: Itô’s formula8m
Week 7.8: Calculation of stochastic integrals using the Itô formula. Black-Scholes model6m
Week 7.9: Vasicek model. Application of the Itô formula to stochastic modelling5m
Week 7.10: Ornstein-Uhlenbeck process. Application of the Itô formula to stochastic modelling.4m
1 practice exercise
Stochastic integration12m
Week
8
2 hours to complete

Week 8: Lévy processes

Upon completing this week, the learner will be able to understand the main properties of Lévy processes; construct a Lévy process from an infinitely-divisible distribution; characterize the activity of jumps of a given Lévy process; apply the Lévy-Khintchine representation for a particular Lévy process and understand the time change techniques, stochastic volatility approach are other ideas for construction of Lévy-based models....
10 videos (Total 94 min), 1 quiz
10 videos
Week 8.2: Examples of Lévy processes. Calculation of the characteristic function in particular cases17m
Week 8.3: Relation to the infinitely divisible distributions7m
Week 8.4: Characteristic exponent8m
Week 8.5: Properties of a Lévy process, which directly follow from the existence of characteristic exponent7m
Week 8.6: Lévy-Khintchine representation and Lévy-Khintchine triplet-17m
Week 8.7: Lévy-Khintchine representation and Lévy-Khintchine triplet-27m
Week 8.8: Lévy-Khintchine representation and Lévy-Khintchine triplet-38m
Week 8.9: Modelling of jump-type dynamics. Lévy-based models7m
Week 8.10: Time-changed stochastic processes. Monroe theorem9m
1 practice exercise
Lévy processes12m
Week
9
16 minutes to complete

Final exam

This module includes final exam covering all topics of this course...
1 quiz
1 practice exercise
Final Exam16m
4.4
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got a tangible career benefit from this course

Top Reviews

By SSMay 21st 2019

This course has less number of quiz questions but sufficient and well designed questions.

By ZMDec 1st 2018

Well presented course. I enjoyed it and was challenged a great deal. Thank you.

Instructor

Avatar

Vladimir Panov

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...

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