Assume we have a standard Brownian motion $W_t$ as the solution to the following SDE
$dX_t=\mu dt+\varepsilon dW_t$
Which kind of SDE it is? Ito process? For which kind of processes we can say that the drift coefficient and $\varepsilon$ does not depend on time or $X$? I assume that in the standard Brownian motion the increments are independent and do not depend on time. So, why in the literature mostly the coefficients depend on time and $X$?
How can i relate this SDE to the Langevin equation governed on the movement of a massless particle immersed in a flow(Brownian motion)
$0=-\gamma \dot x+f(t)$