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

**URL:** <https://discourse.julialang.org/t/can-the-sde-in-differentialequations-jl-add-two-or-more-different-independent-noise-terms/68227>\
**Category:** General Usage\
**Tags:** sde, differentialequation\
**Created:** [September 15, 2021, 8:04pm UTC](https://discourse.julialang.org/t/can-the-sde-in-differentialequations-jl-add-two-or-more-different-independent-noise-terms/68227 "2021-09-15T20:04:58Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![CRquantum](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/crquantum/32/27824_2.png) [@CRquantum](https://discourse.julialang.org/u/CRquantum)\
**Post date:** [September 15, 2021, 8:04pm UTC](https://discourse.julialang.org/t/can-the-sde-in-differentialequations-jl-add-two-or-more-different-independent-noise-terms/68227/1 "2021-09-15T20:04:58Z")

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

[https://diffeq.sciml.ai/stable/features/noise\_process/](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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**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [September 15, 2021, 9:30pm UTC](https://discourse.julialang.org/t/can-the-sde-in-differentialequations-jl-add-two-or-more-different-independent-noise-terms/68227/2 "2021-09-15T21:30:16Z")

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See nondiagonal noise: [Stochastic Differential Equations · DifferentialEquations.jl](https://diffeq.sciml.ai/stable/tutorials/sde_example/#Example-4:-Systems-of-SDEs-with-Non-Diagonal-Noise)

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<div class="post-metadata">

**Author:** ![CRquantum](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/crquantum/32/27824_2.png) [@CRquantum](https://discourse.julialang.org/u/CRquantum)\
**Post date:** [September 15, 2021, 9:50pm UTC](https://discourse.julialang.org/t/can-the-sde-in-differentialequations-jl-add-two-or-more-different-independent-noise-terms/68227/3 "2021-09-15T21:50:22Z")

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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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<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [September 15, 2021, 9:57pm UTC](https://discourse.julialang.org/t/can-the-sde-in-differentialequations-jl-add-two-or-more-different-independent-noise-terms/68227/4 "2021-09-15T21:57:25Z")

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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.