I am studying Stochastic processes and I am a bit confused on the general approach to their study.
In engineering textbooks a concept called "Mean Squared" Calculus is used to define things like time integration/differentiation/continuity of a Stochastic Process.
How does this interact with Ito integration? It seems Ito integration is focused (loosely speaking) on integration with respect to Brownian motion or some other stochastic process, not time integration.
In addition I haven't found any information on Mean-Squared calculus outside of engineering texts, the Stochastic Processes book(math) I have read doesn't even mention it.
So what's going on? Is Mean-Squared Calculus a mathematically recognized theory? Why don't math-books focused on Stochastic Processes use it?