Can someone explain to me the rigorous meaning of statements like: dt^2 = 0 dW*dt = 0 dW^2 = dt Here W = W(t) is standard Brownian motion. I know that a SDE such as dX = f dW + g dt rigorously means [tex]X(t) = X(0) + \int_0^tfdW + \int_0^tgds[/tex] But what does dt^2 mean? And why is it equal to 0. Same with the other statements. Is the above definition useful for this?