Institution: National Research University Higher School of Economics
Start Date: June 25, 2018
The National Research University Higher School of Economics is organizing a free online course named as “Stochastic Processes”. It is assumed that the students are familiar with the basics of probability theory.
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. Register on June 25, 2018, for this course.
- Duration: 8 weeks
- Commitment: 6-8 hours per week
- Subject: Math and Logic
- Institution: National Research University Higher School of Economics
- Languages: English
- Price: Free
- Session: June 25, 2018
- Requirement: Undergraduate students
- Certificate Available: Yes
Who Developed the Course
The 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.
This course is primarily aimed at 3-4th-year undergraduate students, probably 1st-year master’s students.
Where Could This Lead You
After completing this course, you can apply for jobs in the given fields:
Get Extra Benefits
Get a verified certificate to highlight the knowledge and skills you acquire ($29 USD)
- Official and approved-Get a certificate with the logo of the institution and the signature of a professor to show your achievements and increase your professional prospects
- Easy to share-Add the certificate to your résumé or resume, or publish it directly on LinkedIn
- Proven motivational measure-Give yourself an additional stimulus to complete the course
How to Join This Course
You can register yourself here.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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 the construction of various stochastic models.
- 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.
By the end of the course, you’ll be able to:
- Understanding the most important types of stochastic processes (Poisson, Markov, Gaussian, Wiener processes and others) and ability to find the most appropriate process for modeling in particular situations arising in economics, engineering, and other fields;
- Understanding the notions of ergodicity, stationarity, stochastic integration; application of these terms in the context of financial mathematics;
Who Will You Learn With?
Vladimir Panov: Assistant Professor Faculty of economic sciences, HSE
- Importance of Course: At the end of the course, you will gain the theoretical knowledge and practical skills, which are necessary for the analysis of stochastic dynamical systems in economics, engineer, ng and other fields.
- Importance of Certificate: By the Certificate of Achievement you will be able to prove your success when applying for jobs or courses. You can display it on your LinkedIn or CV.
For more information about the course, you may visit the Website.Apply Now