I have system of `N`

coupled stochastic differential equations, that looks like

\displaystyle\frac{du_i}{dt}=F(u_i)+\eta_i

here F is the function that mixes u_i with u_j. The quantity \eta_i is so-called white noise with properties \langle \eta_i(t)\rangle =0, \langle \eta_i(t)\eta_j(t')\rangle=2D\delta(t-t')\delta_{ij}. I try to solve this system in Julia. I define two functions,

```
function deterministic_u!(du, u, p, t)
du .= ...
end
```

```
function noise!(du, u, p, t)
du = sqrt(2)
end
```

When I define `noise!`

function I assume that it coresponds to D=1 case. Then I construct `SDEProblem`

with this functions and a given initial conditions,

```
prob = SDEProblem(deterministic_u!, noise!, u0, tspan, p);
```

However, I obtain results that contradict my computations by hand. I have checked this topic but I still do not understand properly: when I want to add *white noise* should I use diagonal noise or scalar noise?