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!
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.