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?
Best Answer
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.