time dependent a/drift and b/noise terms

[sdementen]

If we want to have $dX = sigma(t) * dWt$, should we just add an extra variable $dt = 1 *dt$ and then use this variable as time ?
For instance,

# x[0] = time, x[1] = X, dX = (cos(t)+1.1) * dWt
pychastic.sde_problem.SDEProblem(
   lambda x: jnp.array([1., 0.]),
   lambda x: jnp.array([[0, 0], [0, (jnp.cos(x[0]) + 1.1)]]),
   x0=[0, 1],
   tmax=10,
)

It works as expected but would it be better to have for drift and noise, a signature like lambda t,x: ... ?

[RadostW]

Implementing higher order schemes for nonautonomous equations are much more involved. This is a deliberate design choice to ease development.

[sdementen]

and does the trick of adding the time dimension work ? or is it highly unstable ?
and is the complexity for nonautonomous equations independent of the noise/drift expressions (for instance if they are linear in the other variables or even constant in the other variables, i.e. only time dependent) ?

[sdementen]

without understanding everything ;-)
https://chat.openai.com/share/2394db4e-d330-4c70-88cb-5038bed14a99