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I'm a first-semester mathematics student, however I already feel the need of a certain goal, or rather an area I'd like to specialize in. For a quite a while, that's been the study of stochastic processes.

Therefore I'd like to ask you what would be the required knowledge and skills in order to begin my study (that would be the main question), but I'd also be very glad to receive any general advices and hints, or maybe even reasons why I shouldn't go for stochastic processes (who knows :)

Thanks a lot for any responses!

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If you want to do stochastic analysis, make sure you have a very solid grounding in classical analysis. The proofs are generally analogies to the proofs in the classical setting with an additional layer of complexity on top o fit because of the stochastic structure. – Chris Janjigian Nov 28 '12 at 21:04
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Apart from probability theory, you should probably do some measure theory and functional analysis before starting out on stochastic processes (SP). Of course, you should also be familiar with vector/matrix formalism from linear algebra. But as a first-semester student you are probably learning this right now.

I don't know any reason why you shouldn't go for SP. I think it's a terrific field with a huge amount of applications (medicine, engineering, economics, etc.). For example, in my master's thesis I used SP to predict regional electricity demand.

I suggest you just get an introductory book on SP (e.g. this) from your university's library and skim through it. Don't worry, if it's hard. It should still give you a clearer impression of required prerequisites, central topics and applications. A more recent book ideally also tells you about current fields of research within SP. For a start you might want to have a look at some lecture notes, e.g. these.

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Thanks for the comprehensive answer! Especially the lecture notes look great (and accessible). – Dahn Jahn Nov 29 '12 at 12:23

I'm a second year undergraduate, and I have only taken a college-level probability course, yet I am in Applied Stochastic Processes this semester, and it is a very accessible class. To get into the theory of stochastic processes, see begeistzwerst's answer, but otherwise if you would like to get a feel for how they are applied at a relatively elementary level (birth and death chains, queueing, basic martingale theory) then I would say that the only prerequisite knowledge would be ay university probability course.

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Thanks for the answer! – Dahn Jahn Nov 29 '12 at 12:15

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