noise kwarg for SDEProblem(f::SDESystem)

[ChristophHotter]

Creating an SDEProblem from a SDEFunction allows specifying the noise process as a kwarg.
Is there a way to specify the noise if I want to create a SDEProblem from a SDESystem? Maybe the noise kwarg could also be added to the SDEProblem function for SDESystems?

[AayushSabharwal]

It should just be propagated if you provide the keyword argument

[ChristophHotter]

I think it is not propagated correctly.
If I provide the kwarg noise=W in the SDEProblem, the noise is unchanged afterwards.

Here is an example, which shows that:

using StochasticDiffEq
using ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D

@parameters σ ρ β
@variables x(t) y(t) z(t)

u0 = [1.0, 0.0, 0.0]
T = (0, 5.0)

eqs = [D(x) ~ σ*(y-x),
       D(y) ~ x*(ρ-z)-y,
       D(z) ~ x*y - β*z]
noiseeqs = [3,
            3,
            3]
@named sde_lorentz = SDESystem(eqs,noiseeqs,t,[x,y,z],[σ,ρ,β]; tspan = T)
sde_lorentz_c = complete(sde_lorentz)

ps = [σ, ρ, β]
p0 = [10, 28.0, 8/3]
parammap = ps .=> p0

W = StochasticDiffEq.RealWienerProcess(0.0, 0.0, 0.0; save_everystep=true)
prob_sde_lorenz = SDEProblem(sde_lorentz_c, u0, T, parammap; noise=W)

sol = solve(prob_sde_lorenz, SRIW1())

@show W