À propos de ce cours
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Niveau intermédiaire

Approx. 28 heures pour terminer

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

Anglais

Sous-titres : Anglais

100 % en ligne

Commencez dès maintenant et apprenez aux horaires qui vous conviennent.

Dates limites flexibles

Réinitialisez les dates limites selon votre disponibilité.

Niveau intermédiaire

Approx. 28 heures pour terminer

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

Anglais

Sous-titres : Anglais

Programme du cours : ce que vous apprendrez dans ce cours

Semaine
1
2 heures pour terminer

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 vidéos (Total 88 min), 1 quiz
12 vidéos
Welcome1 min
Week 1.1: Difference between deterministic and stochastic world4 min
Week 1.2: Difference between various fields of stochastics6 min
Week 1.3: Probability space8 min
Week 1.4: Definition of a stochastic function. Types of stochastic functions.4 min
Week 1.5: Trajectories and finite-dimensional distributions5 min
Week 1.6: Renewal process. Counting process7 min
Week 1.7: Convolution11 min
Week 1.8: Laplace transform. Calculation of an expectation of a counting process-17 min
Week 1.9: Laplace transform. Calculation of an expectation of a counting process-26 min
Week 1.10: Laplace transform. Calculation of an expectation of a counting process-38 min
Week 1.11: Limit theorems for renewal processes14 min
1 exercice pour s'entraîner
Introduction & Renewal processes12 min
Semaine
2
2 heures pour terminer

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 vidéos (Total 89 min), 1 quiz
17 vidéos
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 min
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 min
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 min
Week 2.5: Memoryless property5 min
Week 2.6: Other definitions of Poisson processes-13 min
Week 2.7: Other definitions of Poisson processes-24 min
Week 2.8: Non-homogeneous Poisson processes-14 min
Week 2.9: Non-homogeneous Poisson processes-24 min
Week 2.10: Relation between renewal theory and non-homogeneous Poisson processes-14 min
Week 2.11: Relation between renewal theory and non-homogeneous Poisson processes-27 min
Week 2.12: Relation between renewal theory and non-homogeneous Poisson processes-34 min
Week 2.13: Elements of the queueing theory. M/G/k systems-19 min
Week 2.14: Elements of the queueing theory. M/G/k systems-25 min
Week 2.15: Compound Poisson processes-16 min
Week 2.16: Compound Poisson processes-26 min
Week 2.17: Compound Poisson processes-33 min
1 exercice pour s'entraîner
Poisson processes & Queueing theory14 min
Semaine
3
1 heure pour terminer

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 vidéos (Total 73 min), 1 quiz
7 vidéos
Week 3.2: Matrix representation of a Markov chain. Transition matrix. Chapman-Kolmogorov equation11 min
Week 3.3: Graphic representation. Classification of states-110 min
Week 3.4: Graphic representation. Classification of states-24 min
Week 3.5: Graphic representation. Classification of states-37 min
Week 3.6: Ergodic chains. Ergodic theorem-16 min
Week 3.7: Ergodic chains. Ergodic theorem-215 min
1 exercice pour s'entraîner
Markov Chains12 min
Semaine
4
2 heures pour terminer

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 vidéos (Total 87 min), 1 quiz
8 vidéos
Week 4.2: Gaussian vector. Definition and main properties19 min
Week 4.3: Connection between independence of normal random variables and absence of correlation13 min
Week 4.4: Definition of a Gaussian process. Covariance function-15 min
Week 4.5: Definition of a Gaussian process. Covariance function-210 min
Week 4.6: Two definitions of a Brownian motion18 min
Week 4.7: Modification of a process. Kolmogorov continuity theorem7 min
Week 4.8: Main properties of Brownian motion6 min
1 exercice pour s'entraîner
Gaussian processes12 min
Semaine
5
2 heures pour terminer

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 vidéos (Total 78 min), 1 quiz
8 vidéos
Week 5.2: Two types of stationarity-28 min
Week 5.3: Spectral density of a wide-sense stationary process-17 min
Week 5.4: Spectral density of a wide-sense stationary process-24 min
Week 5.5: Stochastic integration of the simplest type10 min
Week 5.6: Moving-average filters-15 min
Week 5.7: Moving-average filters-212 min
Week 5.8: Moving-average filters-38 min
1 exercice pour s'entraîner
Stationarity and linear filters12 min
Semaine
6
1 heure pour terminer

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 vidéos (Total 53 min), 1 quiz
4 vidéos
Week 6.2: Ergodicity of wide-sense stationary processes15 min
Week 6.3: Definition of a stochastic derivative11 min
Week 6.4: Continuity in the mean-squared sense9 min
1 exercice pour s'entraîner
Ergodicity, differentiability, continuity10 min
Semaine
7
2 heures pour terminer

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 vidéos (Total 82 min), 1 quiz
10 vidéos
Week 7.2: Integrals of the type ∫ f(t) dW_t-113 min
Week 7.3: Integrals of the type ∫ f(t) dW_t-211 min
Week 7.4: Integrals of the type ∫ X_t dW_t-15 min
Week 7.5: Integrals of the type ∫ X_t dW_t-214 min
Week 7.6: Integrals of the type ∫ X_t dY_t, where Y_t is an Itô process6 min
Week 7.7: Itô’s formula8 min
Week 7.8: Calculation of stochastic integrals using the Itô formula. Black-Scholes model6 min
Week 7.9: Vasicek model. Application of the Itô formula to stochastic modelling5 min
Week 7.10: Ornstein-Uhlenbeck process. Application of the Itô formula to stochastic modelling.4 min
1 exercice pour s'entraîner
Stochastic integration12 min
Semaine
8
2 heures pour terminer

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 vidéos (Total 94 min), 1 quiz
10 vidéos
Week 8.2: Examples of Lévy processes. Calculation of the characteristic function in particular cases17 min
Week 8.3: Relation to the infinitely divisible distributions7 min
Week 8.4: Characteristic exponent8 min
Week 8.5: Properties of a Lévy process, which directly follow from the existence of characteristic exponent7 min
Week 8.6: Lévy-Khintchine representation and Lévy-Khintchine triplet-17 min
Week 8.7: Lévy-Khintchine representation and Lévy-Khintchine triplet-27 min
Week 8.8: Lévy-Khintchine representation and Lévy-Khintchine triplet-38 min
Week 8.9: Modelling of jump-type dynamics. Lévy-based models7 min
Week 8.10: Time-changed stochastic processes. Monroe theorem9 min
1 exercice pour s'entraîner
Lévy processes12 min
Semaine
9
16 minutes pour terminer

Final exam

This module includes final exam covering all topics of this course...
1 quiz
1 exercice pour s'entraîner
Final Exam16 min
4.4
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Meilleurs avis

par ZMDec 1st 2018

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

Enseignant

Avatar

Vladimir Panov

Assistant Professor
Faculty of economic sciences, HSE

À propos de Université nationale de recherche, École des hautes études en sciences économiques

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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