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National Research University Higher School of Economics

課程信息

4.3

39 個評分

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12 個審閱

The purpose of this course is to equip students with theoretical knowledge and practical skills, which are necessary for the analysis of stochastic dynamical systems in economics, engineering and other fields.
More precisely, the objectives are
1. study of the basic concepts of the theory of stochastic processes;
2. introduction of the most important types of stochastic processes;
3. study of various properties and characteristics of processes;
4. study of the methods for describing and analyzing complex stochastic models.
Practical skills, acquired during the study process:
1. understanding the most important types of stochastic processes (Poisson, Markov, Gaussian, Wiener processes and others) and ability of finding the most appropriate process for modelling in particular situations arising in economics, engineering and other fields;
2. understanding the notions of ergodicity, stationarity, stochastic integration; application of these terms in context of financial mathematics;
It is assumed that the students are familiar with the basics of probability theory. Knowledge of the basics of mathematical statistics is not required, but it simplifies the understanding of this course.
The course provides a necessary theoretical basis for studying other courses in stochastics, such as financial mathematics, quantitative finance, stochastic modeling and the theory of jump - type processes....

立即開始，按照自己的計劃學習。

根據您的日程表重置截止日期。

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

字幕：English...

立即開始，按照自己的計劃學習。

根據您的日程表重置截止日期。

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

字幕：English...

Week

1Upon 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 個視頻（共 88 分鐘）, 1 個測驗

Welcome1分鐘

Week 1.1: Difference between deterministic and stochastic world4分鐘

Week 1.2: Difference between various fields of stochastics6分鐘

Week 1.3: Probability space8分鐘

Week 1.4: Definition of a stochastic function. Types of stochastic functions.4分鐘

Week 1.5: Trajectories and finite-dimensional distributions5分鐘

Week 1.6: Renewal process. Counting process7分鐘

Week 1.7: Convolution11分鐘

Week 1.8: Laplace transform. Calculation of an expectation of a counting process-17分鐘

Week 1.9: Laplace transform. Calculation of an expectation of a counting process-26分鐘

Week 1.10: Laplace transform. Calculation of an expectation of a counting process-38分鐘

Week 1.11: Limit theorems for renewal processes14分鐘

Introduction & Renewal processes12分鐘

Week

2Upon 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 個視頻（共 89 分鐘）, 1 個測驗

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分鐘

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分鐘

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分鐘

Week 2.5: Memoryless property5分鐘

Week 2.6: Other definitions of Poisson processes-13分鐘

Week 2.7: Other definitions of Poisson processes-24分鐘

Week 2.8: Non-homogeneous Poisson processes-14分鐘

Week 2.9: Non-homogeneous Poisson processes-24分鐘

Week 2.10: Relation between renewal theory and non-homogeneous Poisson processes-14分鐘

Week 2.11: Relation between renewal theory and non-homogeneous Poisson processes-27分鐘

Week 2.12: Relation between renewal theory and non-homogeneous Poisson processes-34分鐘

Week 2.13: Elements of the queueing theory. M/G/k systems-19分鐘

Week 2.14: Elements of the queueing theory. M/G/k systems-25分鐘

Week 2.15: Compound Poisson processes-16分鐘

Week 2.16: Compound Poisson processes-26分鐘

Week 2.17: Compound Poisson processes-33分鐘

Poisson processes & Queueing theory14分鐘

Week

3Upon 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 個視頻（共 73 分鐘）, 1 個測驗

Week 3.2: Matrix representation of a Markov chain. Transition matrix. Chapman-Kolmogorov equation11分鐘

Week 3.3: Graphic representation. Classification of states-110分鐘

Week 3.4: Graphic representation. Classification of states-24分鐘

Week 3.5: Graphic representation. Classification of states-37分鐘

Week 3.6: Ergodic chains. Ergodic theorem-16分鐘

Week 3.7: Ergodic chains. Ergodic theorem-215分鐘

Markov Chains12分鐘

Week

4Upon 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 個視頻（共 87 分鐘）, 1 個測驗

Week 4.2: Gaussian vector. Definition and main properties19分鐘

Week 4.3: Connection between independence of normal random variables and absence of correlation13分鐘

Week 4.4: Definition of a Gaussian process. Covariance function-15分鐘

Week 4.5: Definition of a Gaussian process. Covariance function-210分鐘

Week 4.6: Two definitions of a Brownian motion18分鐘

Week 4.7: Modification of a process. Kolmogorov continuity theorem7分鐘

Week 4.8: Main properties of Brownian motion6分鐘

Gaussian processes12分鐘

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 communications, IT, mathematics, engineering, and more.
Learn more on www.hse.ru...

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Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

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What is the refund policy?

Is financial aid available?

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