3.2. Gausssian processes 29 of a Gaussian process with a specified covariance function ca n be tricky to prove, and existence of, say, continuous versions or cadlag versions of such processes are usually really hard. Definition 3.1 A Brownian motion is a Gaussian process Xwith T = [0,∞) and with E Xt = 0 ∀0 ≤ t, Cov(Xs,Xt) = s ∀0 ≤ .... "/>