@alexyar Thanks for asking!
The most pressing reason I have for understanding stochastic processes in general (which will probably involve learning some Ito calculus) is that the next interpretation/version of quantum mechanics I want to understand is the Nelson-Yasue “stochastic quantization” approach, which has a lot in common with the Bohmian approach I've been studying this year but seems more promising for understanding what theory orthodox quantum mechanics could be a coarse-graining of. My acquaintance (friend in the making?) Maaneli Derakhshani has written a pair of papers on this subject [1] [2].
But it’s also of interest to me because my cognitive science research has led me to the conclusion that I need to understand dissipative systems better (free energy dissipation/minimization bridges the gap between physical brain processes and information-theoretic cognitive/inferential processes via variational Bayes - see Friston’s work, e.g. this), and stochastic calculus seems well-suited to modeling dissipative systems.
As a bonus, I will probably end up learning some things about finance that could be useful down the line.