Itô processes
An Itô process is commonly written
\[dX_t=a(X_t,t)dt+b(X_t,t)dW_t.\]More precisely, this notation represents the integral equation
\[X_t=X_0+\int_0^t a(X_s,s)\,ds+\int_0^t b(X_s,s)\,dW_s.\]The second integral is an Itô stochastic integral. Its construction differs from ordinary Riemann integration because Brownian paths are not differentiable.
Key idea. SDE notation is shorthand for an equation containing both an ordinary time integral and a stochastic integral.