Hi all!

I am newbie to julia and I am playing with it to solve SDE systems, numerically.

I had a look at Non-diagonal noise Tutorial (Example No. 4) https://diffeq.sciml.ai/stable/tutorials/sde_example/, but still something is not clear for me which I explain below:

Lets assume that we have two coupled SDEs

dx1 = a11*x1*dt + a12*x2*dt + dw1

dx2 = a21*x1*dt + a22*x2*dt + dw2

a_ij’s here are all state dependent. dw1 and dw2 have Non-diagonal, state dependent (x1 and x2 dependent) cross-correlation so that we can generally say:

dw_i*dw_i = b_ij dt

where b_ij is the element-wise representation of noise correlation matrix:

How should one solve this sort of problem using non-diagonal noise option in julia?

Which solver is recommended?