提供方

National Research University Higher School of Economics

课程信息

4.3

39 个评分

•

12 个审阅

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....

立即开始，按照自己的计划学习。

根据您的日程表重置截止日期。

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

字幕：English...

立即开始，按照自己的计划学习。

根据您的日程表重置截止日期。

建议：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 个视频（共 88 分钟）, 1 个测验

Welcome1分钟

Week 1.1: Difference between deterministic and stochastic world4分钟

Week 1.2: Difference between various fields of stochastics6分钟

Week 1.3: Probability space8分钟

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

Week 1.5: Trajectories and finite-dimensional distributions5分钟

Week 1.6: Renewal process. Counting process7分钟

Week 1.7: Convolution11分钟

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

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

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

Week 1.11: Limit theorems for renewal processes14分钟

Introduction & Renewal processes12分钟

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 个视频（共 89 分钟）, 1 个测验

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分钟

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分钟

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分钟

Week 2.5: Memoryless property5分钟

Week 2.6: Other definitions of Poisson processes-13分钟

Week 2.7: Other definitions of Poisson processes-24分钟

Week 2.8: Non-homogeneous Poisson processes-14分钟

Week 2.9: Non-homogeneous Poisson processes-24分钟

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

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

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

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

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

Week 2.15: Compound Poisson processes-16分钟

Week 2.16: Compound Poisson processes-26分钟

Week 2.17: Compound Poisson processes-33分钟

Poisson processes & Queueing theory14分钟

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 个视频（共 73 分钟）, 1 个测验

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

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

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

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

Week 3.6: Ergodic chains. Ergodic theorem-16分钟

Week 3.7: Ergodic chains. Ergodic theorem-215分钟

Markov Chains12分钟

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 个视频（共 87 分钟）, 1 个测验

Week 4.2: Gaussian vector. Definition and main properties19分钟

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

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

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

Week 4.6: Two definitions of a Brownian motion18分钟

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

Week 4.8: Main properties of Brownian motion6分钟

Gaussian processes12分钟

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...

我什么时候能够访问课程视频和作业？

注册以便获得证书后，您将有权访问所有视频、测验和编程作业（如果适用）。只有在您的班次开课之后，才可以提交和审阅同学互评作业。如果您选择在不购买的情况下浏览课程，可能无法访问某些作业。

我购买证书后会得到什么？

您购买证书后，将有权访问所有课程材料，包括评分作业。完成课程后，您的电子课程证书将添加到您的成就页中，您可以通过该页打印您的课程证书或将其添加到您的领英档案中。如果您只想阅读和查看课程内容，可以免费旁听课程。

退款政策是如何规定的？

有助学金吗？

还有其他问题吗？请访问 学生帮助中心。