# What are the minimum and maximum prerequisites to study Stochastic Processes?

Suppose, I never studied random variables. This is the syllabus:

Lecture contents

Review of important notions of probability theory (4h).

A few remarks on stochastic processes : Definition of a Stochastic process, Notion of the state and realization of the process, Classification of Stochastic processes.Probability and Moment generating functions and their properties (2h).

Branching processes Galton process :Probability of extinction , Applications in demography and nuclear physics (4h).

Poisson processes and its applications. Exponentioal distribution and its properties, . Poisson Process and their properties : Distribution of periods between successive calls , Summing independent Poisson processes, Conditional distributions of inter-arrival times , Generalizations of Poisson processes , nonuniform distribution , Composed Poisson process (6h).

Simple queuing systems: M/M/c systems without and with queue.: Probability of blocking, probability of the delay and average waiting time (4h).

Renewal Processes (6h).

Review (4h).

What are the minimum and maximum prerequisites to study Stochastic Processes?

That is, what things should I know beforehand to start studying Stochastic Processes?

• If you have never studied random variables, it will be close to impossible. What is your background in probability theory? – luka5z Oct 6 '15 at 21:02
• If you have a "basic working knowledge" of random variables. rest assured that you do not have the necessary background to get a "basic working knowledge" of stochastic processes in a week. This is, for the most part, true even if you actually took a course based on a text with a title such as Probability and Statistics for Engineers (or for Scientists and Engineers). These types of books are mostly about statistics, typically consist of just a lot of cookbook formulas about buzzwords such as $t$-tests and $z$-scores and $p$-values. – Dilip Sarwate Oct 6 '15 at 21:47
• @anonymouse - your best try is wikipedia en.wikipedia.org/wiki/Stochastic_process – luka5z Oct 7 '15 at 7:09
• Are you good with basic probability theory?? Info is required? If no then follow this if you would like to start from the basics link math.stackexchange.com/questions/31838/… . You dont have to study whole things in the text book but the central concepts(be good at it) and skip other things(if you dont have sufficient time) – Jasser Dec 28 '15 at 15:17

You have basically answered your own question. Random variables are the single most important prerequisite to start learning about processes. And underneath that, basic probability theory (the infinite kind, based on $\sigma$-algebras).

Apart from that it depends on what kinds of processes are going to be the focus of your study or work. For finite-state, discrete-time processes some matrix calculus might come in handy. For continuous-time real-valued processes you want to review calculus and the properties of the real numbers.

Based on the course description I recommend the first chapters (say, 2 and 3) of Arnold Allen, Probability, Statistics, and Queueing Theory. A bit superficial on the basic probability stuff but you don't want to spend 20 hours preparing for a 4h lecture, right? Bonus: chapters 4 and 5 seem to match some of your course content rather nicely.

• " first chapters of Arnold Allen, Probability, Statistics, and Queuing Theory. " --- First Chapter or First Part? – user6704 Dec 31 '15 at 1:49
• I have made the recommendation more specific now. – Justpassingby Dec 31 '15 at 8:02

I had been absent from the university for >10 years and made a comeback this semester starting with a course about stochastic processes.

I bought the book "Schaum's Outline of Probability, Random Variables, and Random processes" by Hwei P. Hsu and made the exercises of the first 4 chapters and some exercises in the other chapters and after that i had no problems during the course.

• "some exercises in the other chapters " --- which other chapter? – user6704 Dec 27 '15 at 17:39
• @anonymous Well, those chapters are usually part of the course and not really necessary to do before the course starts but if you want to be well prepared spend some time studying chapter 5, 6 and 9. 5 is Random processes, 6 is Analysis and processing of random processes and 9 is Queueing theory. – JKnecht Dec 27 '15 at 18:16
• @anonymous I can add that the book has solutions to almost every exercise which is nice. – JKnecht Dec 27 '15 at 18:16
• Just curious, why did you need to come back to the university after >10 years? – user6704 Dec 27 '15 at 22:53
• @anonymous I didnt need to. I left the university because i got a good job. Then i had a career there and retired just a few months ago. Now i am back at the university just because its fun. – JKnecht Dec 28 '15 at 7:23