How to integrate a multi dimensional SDE forced by the same source of noise?

New to Julia
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1

Hi everyone for my research I need to integrate an SDE system of this kind:

dx=f1(x,y)dt + g1(x,y)dW
dy=f2(x,y)dt + g2(x,y)dW

My issue is that I want the Winer noise dW to be exactly the same for the two variable. I wanted to take advantage over DifferentialEquation.jl but I can really find in the documentation the way to specify this particular case to SDEProblem. I’m sure it must be related to the option NoiseProcess but I had no luck.
Thanks for your help!

2

That’s a scalar noise SDE. There is an example of this in the tutorials.

https://docs.sciml.ai/DiffEqDocs/stable/tutorials/sde_example/#Example-3:-Systems-of-SDEs-with-Scalar-Noise