# Stochastic Processes…what is it?

My university is offering stochastic processes next semester, here is the course description:

Review of distribution theory. Introduction to stochastic processes, Markov chains and Markov processes, counting, and Poisson and Gaussian processes. Applications to queuing theory.

I'm torn between this course and analysis 2. I'm not sure what stochastic processes deals with, and the description doesn't help. Can anyone explain what you do in such a course? Is it proofs-based? Also, would you recommend this over Analysis 2?

Thanks.

• I guess it is an undergraduate course? – Jean-Sébastien Dec 4 '12 at 18:46
• @Jean-Sébastien Yes it is – A A Dec 4 '12 at 18:47
• What is Analysis 2? – Did Dec 4 '12 at 18:47
• Why not ask the instructor, or a student who has previously taken it? – Nate Eldredge Dec 4 '12 at 19:22
• My guess: If done rigorously, the above-described course on stochastic processes will require the sort of maturity you'll find in the "Analysis 2" mentioned above, so I'd recommend taking the analysis course first. If not done rigorously, then it may be a fun course (not that rigour isn't fun, but I mean you'll probably skip over some proof details to see more breadth of stuff), so it wouldn't require the "Analysis 2". The only way to find out is to ask the instructor(s) or former students, as Nate Eldredge says. – ShreevatsaR Dec 4 '12 at 19:25

## 2 Answers

In our curriculum Stochastic comes after Analysis 2. This definitely makes sense since Analysis 2 provides a broad fundamentum for a lot of mathematical topics and Stochastic needs tools from Analysis 2 when you get to multidimensional continuous problems like Gaussian processes. So I would recommend you Analysis 2.

"Stochastic" refers to topics involving probability -- often the treatment of processes that are inherently random in nature by virtue of being some sot of random function about a random or deterministic variable, or a process parameterized by a random quantity.

For example, Brownian motion is a stochastic process; similarly, the behavior of a LTI system containing a random parameter is a stochastic process (say, the vibration of a spring-mass system, where the spring constant is actually a random variable).

Stochastic calculus requires a strong background in analytical probability theory, which itself requires some notion of measure theory, algebra, and multivariable analysis. Many undergraduate courses will avoid some of the rigorous elements of stochastic analysis, but to really understand it, you will need a decent background in undergraduate analysis through multivariable analysis, Lebesgue theory, and measure theory.

In short, take Analysis II, take Probability, and then consider Stochastic processes if you are interested in it.