Back to Stochastic processes

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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.
Do you have technical problems? Write to us: coursera@hse.ru...

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Apr 29, 2021

This course is a really good course if you want to learn about stochastic processes. But, you need to have some prerequisite knowledge, especially about probability theory and calculus.

RK

Nov 15, 2020

This is really a very good course. I wish there was a second course on the same topic going into a much deeper level for Makov Processes, Martingales and Stochastic Integration.

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By Letao Z

•Jun 19, 2018

I do believe the lecturer is incapable in Mathematics, even cannot give clear definitions...1) Mathematical concepts were not stated clearly... Even definitions are messed up (i.e. the lecture does not list all conditions needed for a concept...).. e.g. the definition for Fourier/inverse Fourier transform (not correct); Definition for ergodic is not right (there are a lot of definitions for ergodic Markov Processes., depending on the type of processes.) It's fine the the instructor only uses one of them, but he does not specify what conditions he enforced, even if you used the mean-square sense ergodic, you should SAY it!!2) A lot of repeating lectures. e.g. week7.2 lectures, half of it repeated the proof of "K(s,t) continuous iff K(s,t) continuous along the diagonal" this is identical the lecture 6.4 properties of covariance function.3) a lot of errors in homework questions! Even in questions in each video... Not just one, but a ton of them. Please, there are only 6 questions in a quiz and 5 of them have wrong answers... It could only tell how sloppy or how incapable the instructor is 4) As for the content, it is really just an introductory course. If the purpose was to introduce topics in stochastic processes, can you please at least state the definitions correctly and clearly? If the purpose was to focus on one of the most important stochastic process -- Brownian Motion, there isn't any important part emphasized in the course, even not a proof from Random walk to 1-d Brownian motion... 5) The last thing (just my complaint), is that the pen he used is really squeaky...errrrrr

By Paul K

•Nov 21, 2018

This is an excellent course for learning the theory of stochastic processes. I have taken many courses with Coursera and to me this ranks as one of their best. It is a difficult course and covers a lot of material but I found it to be a very well developed and well-presented course. After completion I feel that I significantly improved both my knowledge and understanding of stochastic processes and probability theory.

The professor is very engaging in the lectures and employs a classical style of teaching theoretical mathematics. Theorem, proof explanation, example, theorem, proof, explanation, example pretty much right from his head to the clear board. No software is needed though I found it helpful to simulate some processes to see how they worked or to do equation solving but it is not required. Although English is not the professor’s first language this was not a problem for me although it did cause some problems for the speech to text converter that Coursera uses. It didn’t matter too much as in my opinion the professor has excellent teaching skills and provides lucid explanations to some very difficult concepts. A few times there might be some elements of a proof left out due to rushing or mistakes made in them but this was not very often and they often got sorted out in the discussion sections. Still this is a course that puts a lot of demands on the student regardless of how perfect a lecture may be. It is just the nature of the subject material. It is the closest thing to a graduate course I have taken at Coursera and it should be considered as an advanced course rather than intermediate. Some background in probability and measure theory would be very helpful to a student as the professor makes use of it during the lectures. Some background on it is provided but I found I had to do some investigation of it on my own even having studied it some in the past.

The course was a bit short on resources so I included some links to web sites and book pdf's that I found useful which can be found in the Week One Discussion Forum.

Some things I noted: The quizzes are often learning exercises not simply a recitation of facts learned in the lectures. I found the threads in the discussion forums for each week very useful as they contain some history of discussions of various problems in the course.

I highly recommend this course to any students who are seeking to improve their understanding of stochastic processes and probability theory or for strengthening their understanding of other fields of statistics that are based on time dependence like time series analysis.

By Igor K

•May 19, 2018

The lecture rash in the material if you are not expert in convergences, sigma algebra, and many intermediate statements of probability it will hard to follow this running,

The lecture reread material and do not build intuition, I found this course as wasting time

By Dmitry G

•Jul 21, 2018

Semi-rigorous and rather sketchy presentation of the subject, which is good for developing initial intuition. Very good for initial introduction into Stochastic processes for people already familiar with probability theory. The main drawback - lack of good illustrative physical and financial examples and proofs of big theorems. From a technical side - the course is still underdeveloped: ton of mistakes in answers for quizes, repetition of lecture material in one or other forms, not very interesting exercises. Hope all this problems would be solved, and the course will serve as laconic intro into the subject for a lot of people.

By Charles R

•Sep 14, 2019

This was helpful but I still feel I don't understand stochastic processes. Folks taking this course should know that it's pretty tough, compared to most Coursera courses.

By Harsh S

•Jan 4, 2019

Theoretical course , practical examples should be more

By Pengchong L

•Sep 11, 2018

Underdeveloped: Lots of mistakes, lacks of intuition, no explanation whatsoever of quiz questions.

By Dmitry Z

•Dec 25, 2018

The course is remarkable in that it encompasses a wide range of topics and delivers them in a structured and accessible way with virtually no effect on mathematical rigour. I liked this course more than the one I had in my university because it gave me intuition about stochastic processes and a basic framework using which I can now solve real-world problems. I would appreciate more practical tasks and more active forum discussions though.

By 夏旸

•Nov 17, 2018

The content is very sufficient but if the class hour could be extended to about 30-50% more, it will help learners like me concretely understand the content within the class without referring to much more information and notes from other universities. By the way, it's good to learn things like Ito formula and Levy process in this class. Thank for the efforts made by Prof. Panov.

By mohammadmahdiabdollahpour

•Mar 30, 2019

It is a good course on theory side so many nice and neat theorems an proofs but I think there needs to be some sections devoted to demonstrate applications of stochastic processes with detail. there was some of these examples but it can be more and it should exist at least for each week topic expect for some weeks.

By James L

•Nov 12, 2018

Good course. A bit heavy on the theory side but if you can absorb the theory the practitioner's side is that much easier. The last topic of the course was Levy processes so the course ended just as it was getting interesting (that's not a complaint but a compliment). Would be interested in a follow-up to the course (eg. Stochastic Processes II) to expand on concepts for quantitative finance.

By Fernando T

•Aug 9, 2018

This was a good course of stochastic poroceses. I found it quite challenging, specially the last two weeks, and i recomend this course to people who at least have taken an introductory class of probabilistic models. Also, I recomend the instrutor to give feedback to the quizes, like giving the answers and short explanations.

By Xinyi J

•Apr 28, 2019

The course is good and but strongly recommend not to study without fundamental knowledge of statistics. Having knowledge like Bayesian statistics will be better I think.

By Daniel F

•Apr 16, 2020

Even after finishing this course I am still feeling a bit ambivalent about it. While there are some parts of the course in which applied concepts are introduced quite vividly, there are other parts where practical examples are widely missing. In certain chapters proofs and more advanced mathematical statements are given. However, the course neither is a typical mathematical introduction to stochastic processes, as there often is a huge lack of mathematical rigorousness and preciseness. Hence, after finishing this course you will have a good overview about a broad variety of topics from the theory of stochastic processes but you will neither really understand the mathematical theory, nor how to apply the concepts.

By Ajit C B

•Oct 11, 2018

I definitely think this course should be categorized as advanced instead of intermediate. The course is mathematically quite rigorous. There are a few bugs in the quizzes and the language of many of the questions can be improved. I enjoyed many of the lectures. In particular, it was nice to connect my lay man notions of some well-known stochastic processes with their precise definitions.

By Крайнев К В

•Jul 22, 2019

Thank you for the course, Vladimir!

It was gentle intro in Stochastic Processes (there's no any other course on this platform. I remember only the course by ФизТех. But I couldn't find it here and it was rather scaring for a beginner)

It would be cool if you could add some more topics in quantitative finance or add some optional exercises. Or the separate course can be created (with coding exercises too).

By Луницин М

•Sep 20, 2018

This course is a good introduction to the theory of stochastic processes.Lecturer explains theory pretty clearly.Sometimes misprints occurs in quizes, but they are not so critical.

By Ramesh K

•Nov 16, 2020

This is really a very good course. I wish there was a second course on the same topic going into a much deeper level for Makov Processes, Martingales and Stochastic Integration.

By Mite

•Sep 23, 2019

Great course! The subject material was well covered and it gave me the tools to tackle more advanced stochastic, like population dynamics or quantitative finance.

By puneet g

•Apr 16, 2020

Vladimir did a wonderful job. Your course is too good. Request to add more practical problems.

By Wei T

•Apr 25, 2019

It's great for a beginner to learn the basic ideas about stochatic processes.

By Stephen F

•Jun 26, 2019

If you are looking to review concepts this course is fine; however, the mathematics surrounding the proofs is hastily presented and skips several steps. I would say the course is taught at a level beyond that of a student enrolled in a Master's in Statistics.

By Zixu Z

•May 3, 2020

The course is of mixed experiences. I enjoyed the clear derivations and proofs. However, after introducing a lot of seemly important concepts and spending a lot of time in proofs, there are barely any content on why we are doing these. OK, I got it that things like ergodicity, spectral functions seems important since the instructor spent more than half an hour showing the proofs and properties, but then the instructor stopped without mentioning anything about if a stochastic process is ergodic, then what? To me, I learned many new fancy terms but still have little ideas of how it can be helpful if I try to look at a stock price process, for example.

By Samyak J

•May 29, 2020

Good course, but the theory is sometimes ill-explained or skipped. Also, it would be a lot better if there were more examples and practical questions.

By Long Y

•Jun 15, 2018

Too many errors in the quiz. It makes students confused about what is asked and why the answer is that. Students keep guessing what the question is asking or what typo the correct answer may have.

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