I was studying the SDE and their numerical implementation. In every SDE, the randomness is accounted for by Brownian motion and the Euler-Maruyama method, and higher-order methods are derived with Brownian motion (the Ito integral is evaluated wrt Brownian motion). If however the randomness is modeled not by Brownian motion but some color noise (eg, white, pink, etc). Does the Euler-Maruyama scheme still hold? Or do we need to rederive such numerical schemes? or model the random 'force' in terms of Brownian motion and then use the E-M method?
I would really appreciate any help. Thank you!