Can the Euler-Maruyama method be used to simulate Langevin equations for non-Gaussian white noise? I need to evaluate a Langevin equation of the form $$ dx= a(x)dt+D \eta dt$$ where $\eta$ is a non-Gaussian white noise.
In general, stochastic differential equations have no assumptions on distribution of the stochastic variables. However care must be taken for proper solution (Ito/Stratonovich and other perks of multiplicative noise). Also the equivalence of Langevin equation to approptiate Fokker-Plank equation breaks down, as the Fokker-Plank equation assumes Gaussian noise. Colored noise also must be payed special attention.
I recommend the following books for numerical methods of SDE solution -
- Gardiner, Crispin. Stochastic methods. Vol. 4. Berlin: Springer, 2009
- Kloeden, Peter E., and Eckhard Platen. Numerical solution of stochastic differential equations. Vol. 23. Springer Science & Business Media, 2013.