I'm currently in my last year of my master's degree program "Physics of Complex System". I would like to write my master thesis about stochastic processes, but I'm having trouble in finding a good advisor with a good project within Europe, I'm planning of continuing my education with a Phd. Any advices?
Typically you get your advisor from your own institution. Your university makes the certificate indicating that you are "good". They put their reputation on the line by making that statement. So most universities want some quality control for at least the most central courses, like a thesis.
Also, think of this from the point of view of the advisor. Advising students is work, often enjoyable work, but still work. We usually get assigned students or a number of students we have to take, or we have to teach less other courses if we take x students, or in some other way get told by the department to do this for our own students. If we take outside students, that just adds to our workload, and is not compensated. However, enjoyable advising students is, I can think of even more enjoyable things to do, like playing with my own kids.