Hi everybody,

first of all let me say that I still consider myself new to Julia (and even programming in general), so everything I say and write is likely to contain very naive mistakes. Also, if there is anything I should improve regarding how to post/ask questions, please let me know.

I will first write my final goal, just in case I am approaching it from a completely wrong/super inefficient angle and you know a better way to do it. After that I will write my actual question, which is (I think) much simpler and concerns basic usage of the DifferentialEquations.jl package.

Goal: simulate a system of coupled SDEs, letās say `2N`

, driven by `N`

complex Brownian motions. The first `N`

equations are driven by the `N`

complex Brownian motions, the second `N`

equations are driven by the conjugate of the `N`

Brownian motions.

Strategy: implement a custom noise using DiffEqNoiseProcess.jl. In particular, I want to construct a NoiseTransport process and then use it to drive my system of SDEs.

Problem: I donāt seem to be able to follow the instructions of the documentation. I link below the sections I read the most, but of course I tried to at least skim through all what seemed to be relevant.

`DiffEqNoiseProcess.NoiseTransport`

`Stochastic Differential Equations`

It seems that when it comes to using a NoiseTransport noise, I am not able to implement even a simple Brownian motion. Of course in this case I could just set up my problem as explained by the general tutorial of DifferentialEquations.jl (without the need of DiffEqNoiseProcess.jl), since Brownian motion is already the default noise of SDEProblem(ā¦). The point here is that I am trying to implement the easiest nontrivial NoiseTranport noise I can think of.

Minimal (not working) example:

```
using DifferentialEquations
function f(u,p,t,rv)
rv
end
t0 = 0.0
T = 10
u0 = 0.0
W = NoiseTransport(t0, f, randn)
function drift(u,p,t)
0
end
function diffusion(u,p,t)
1
end
my_prob = SDEProblem(drift, diffusion, u0, (t0,T), noise = W)
my_sol = solve(my_prob)
```

but the values of the solution my_sol are simply zero for all time points.

I hope some of you can point out what I am making wrong.

I am sure I am missing something very obvious, so I apologize in advance.

Thanks,

Damiano