Implementing two different noise processes in a differential equation

Specific Domains Numerics
1

Hi! I’m trying to implement the 3-dim complex valued DE
du/dt = (alpha(t) + beta(t))*u(t)

alpha(t) is a 3-dim OU process and beta(t) is a 1-dim OU process (mean 0) with a given covariance E[beta(t)beta(s)] = f(s,t).

I tried to solve the DE with both SDEProblem and RODEProblem. Both methods work well when there is just one noise, but I don’t know how to implement the DE with two noises.

function f(du, u, p, t, W)
    du .= u .* (W[1] + W[2])
end

W = [alpha, beta]

prob = RODEProblem(f, u0, tspan, noise = W, noise_prototype = zeros(2, 3))

does not work (because W is not 1 process). Also in SDE I don’t know how to do it. Is there another function I could use?

Could someone please help me? Thanks in advance!

2

What you’re describing is just a non-diagonal noise problem. See this tutorial: