And if you really want to explicitly construct the process even though it isn’t necessary I think this works:
# note the initial value is a vector of length two since you need a
# two-dimensional Brownian motion
W = WienerProcess(0.0, [0.0,0.0])
prob = SDEProblem(f!, g!, u0, (0.0,1.0); noise = W, noise_rate_prototype=zeros(3,2))