Can the SDE in DifferentialEquations.jl add two or more different/independent noise terms?

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1

I have looked at the noise terms in SDE in DifferentialEquations.jl

https://diffeq.sciml.ai/stable/features/noise_process/

I am not expert in SDE, and perhaps what I said is wrong and even stupid.
I see all those equations in the link above, on the right hand side, only has one noise term dW.
I wonder, can i add more independent noise terms, like dW2, dW3, etc… ?

Adding more noise terms, the algorithm should be almost the same as just one noise term I believe. For example, I think if use Runge-Kutta, one just need to add corresponding random number in the propagation.

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See nondiagonal noise: Stochastic Differential Equations · DifferentialEquations.jl

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Thank you very much! I guess that’s it!
By the way, have you guys tried Kasdin’s RK4 SDE algorithm?

  1. Jeremy Kasdin,
    Runge-Kutta algorithm for the numerical integration of stochastic differential equations,
    Journal of Guidance, Control, and Dynamics,
    Volume 18, Number 1, January-February 1995, pages 114-120.
  2. Jeremy Kasdin,
    Discrete Simulation of Colored Noise and Stochastic Processes and 1/f^a Power Law Noise Generation,
    Proceedings of the IEEE,
    Volume 83, Number 5, 1995, pages 802-827.

It is a fixed step size method, but perhaps it is not bad.

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I gave a big response in that other thread as to why that method does not converge as well as claimed.

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