Informações sobre o curso
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Aprox. 28 horas para completar

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

Inglês

Legendas: Inglês

100% online

Comece imediatamente e aprenda em seu próprio cronograma.

Prazos flexíveis

Redefinir os prazos de acordo com sua programação.

Nível intermediário

Aprox. 28 horas para completar

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

Inglês

Legendas: Inglês

Programa - O que você aprenderá com este curso

Semana
1
2 horas para concluir

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 vídeos ((Total 88 mín.)), 1 leitura, 1 teste
12 videos
Week 1.1: Difference between deterministic and stochastic world4min
Week 1.2: Difference between various fields of stochastics6min
Week 1.3: Probability space8min
Week 1.4: Definition of a stochastic function. Types of stochastic functions.4min
Week 1.5: Trajectories and finite-dimensional distributions5min
Week 1.6: Renewal process. Counting process7min
Week 1.7: Convolution11min
Week 1.8: Laplace transform. Calculation of an expectation of a counting process-17min
Week 1.9: Laplace transform. Calculation of an expectation of a counting process-26min
Week 1.10: Laplace transform. Calculation of an expectation of a counting process-38min
Week 1.11: Limit theorems for renewal processes14min
1 leituras
Quiz-1 answers and solutions10min
1 exercício prático
Introduction & Renewal processes12min
Semana
2
2 horas para concluir

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 vídeos ((Total 89 mín.)), 1 leitura, 1 teste
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-23min
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-34min
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-44min
Week 2.5: Memoryless property5min
Week 2.6: Other definitions of Poisson processes-13min
Week 2.7: Other definitions of Poisson processes-24min
Week 2.8: Non-homogeneous Poisson processes-14min
Week 2.9: Non-homogeneous Poisson processes-24min
Week 2.10: Relation between renewal theory and non-homogeneous Poisson processes-14min
Week 2.11: Relation between renewal theory and non-homogeneous Poisson processes-27min
Week 2.12: Relation between renewal theory and non-homogeneous Poisson processes-34min
Week 2.13: Elements of the queueing theory. M/G/k systems-19min
Week 2.14: Elements of the queueing theory. M/G/k systems-25min
Week 2.15: Compound Poisson processes-16min
Week 2.16: Compound Poisson processes-26min
Week 2.17: Compound Poisson processes-33min
1 leituras
Quiz-2 answers and solutions10min
1 exercício prático
Poisson processes & Queueing theory14min
Semana
3
2 horas para concluir

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 vídeos ((Total 73 mín.)), 1 leitura, 1 teste
7 videos
Week 3.2: Matrix representation of a Markov chain. Transition matrix. Chapman-Kolmogorov equation11min
Week 3.3: Graphic representation. Classification of states-110min
Week 3.4: Graphic representation. Classification of states-24min
Week 3.5: Graphic representation. Classification of states-37min
Week 3.6: Ergodic chains. Ergodic theorem-16min
Week 3.7: Ergodic chains. Ergodic theorem-215min
1 leituras
Quiz-3 answers and solutions10min
1 exercício prático
Markov Chains12min
Semana
4
2 horas para concluir

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 vídeos ((Total 87 mín.)), 1 leitura, 1 teste
8 videos
Week 4.2: Gaussian vector. Definition and main properties19min
Week 4.3: Connection between independence of normal random variables and absence of correlation13min
Week 4.4: Definition of a Gaussian process. Covariance function-15min
Week 4.5: Definition of a Gaussian process. Covariance function-210min
Week 4.6: Two definitions of a Brownian motion18min
Week 4.7: Modification of a process. Kolmogorov continuity theorem7min
Week 4.8: Main properties of Brownian motion6min
1 leituras
Quiz-4 answers and solutions10min
1 exercício prático
Gaussian processes12min
Semana
5
2 horas para concluir

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 vídeos ((Total 78 mín.)), 1 leitura, 1 teste
8 videos
Week 5.2: Two types of stationarity-28min
Week 5.3: Spectral density of a wide-sense stationary process-17min
Week 5.4: Spectral density of a wide-sense stationary process-24min
Week 5.5: Stochastic integration of the simplest type10min
Week 5.6: Moving-average filters-15min
Week 5.7: Moving-average filters-212min
Week 5.8: Moving-average filters-38min
1 leituras
Quiz-5 answers and solutions10min
1 exercício prático
Stationarity and linear filters12min
Semana
6
1 hora para concluir

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 vídeos ((Total 53 mín.)), 1 leitura, 1 teste
4 videos
Week 6.2: Ergodicity of wide-sense stationary processes15min
Week 6.3: Definition of a stochastic derivative11min
Week 6.4: Continuity in the mean-squared sense9min
1 leituras
Quiz-6 answers and solutions10min
1 exercício prático
Ergodicity, differentiability, continuity10min
Semana
7
2 horas para concluir

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.

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10 vídeos ((Total 82 mín.)), 1 teste
10 videos
Week 7.2: Integrals of the type ∫ f(t) dW_t-113min
Week 7.3: Integrals of the type ∫ f(t) dW_t-211min
Week 7.4: Integrals of the type ∫ X_t dW_t-15min
Week 7.5: Integrals of the type ∫ X_t dW_t-214min
Week 7.6: Integrals of the type ∫ X_t dY_t, where Y_t is an Itô process6min
Week 7.7: Itô’s formula8min
Week 7.8: Calculation of stochastic integrals using the Itô formula. Black-Scholes model6min
Week 7.9: Vasicek model. Application of the Itô formula to stochastic modelling5min
Week 7.10: Ornstein-Uhlenbeck process. Application of the Itô formula to stochastic modelling.4min
1 exercício prático
Stochastic integration12min
Semana
8
2 horas para concluir

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.

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10 vídeos ((Total 94 mín.)), 1 teste
10 videos
Week 8.2: Examples of Lévy processes. Calculation of the characteristic function in particular cases17min
Week 8.3: Relation to the infinitely divisible distributions7min
Week 8.4: Characteristic exponent8min
Week 8.5: Properties of a Lévy process, which directly follow from the existence of characteristic exponent7min
Week 8.6: Lévy-Khintchine representation and Lévy-Khintchine triplet-17min
Week 8.7: Lévy-Khintchine representation and Lévy-Khintchine triplet-27min
Week 8.8: Lévy-Khintchine representation and Lévy-Khintchine triplet-38min
Week 8.9: Modelling of jump-type dynamics. Lévy-based models7min
Week 8.10: Time-changed stochastic processes. Monroe theorem9min
1 exercício prático
Lévy processes12min
Semana
9
16 minutos para concluir

Final exam

This module includes final exam covering all topics of this course

...
1 teste
1 exercício prático
Final Exam16min
4.4
33 avaliaçõesChevron Right

43%

consegui um benefício significativo de carreira com este curso

Principais avaliações do Processos estocásticos

por SSMay 21st 2019

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

por ZMDec 1st 2018

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

Instrutores

Avatar

Vladimir Panov

Assistant Professor
Faculty of economic sciences, HSE

Sobre 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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