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

**URL:** <https://discourse.julialang.org/t/how-to-integrate-a-multi-dimensional-sde-forced-by-the-same-source-of-noise/88988>\
**Category:** New to Julia\
**Tags:** question, diffeq\
**Created:** [October 20, 2022, 2:07am UTC](https://discourse.julialang.org/t/how-to-integrate-a-multi-dimensional-sde-forced-by-the-same-source-of-noise/88988 "2022-10-20T02:07:12Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![giav1n](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/giav1n/32/43708_2.png) [@giav1n](https://discourse.julialang.org/u/giav1n)\
**Post date:** [October 20, 2022, 2:07am UTC](https://discourse.julialang.org/t/how-to-integrate-a-multi-dimensional-sde-forced-by-the-same-source-of-noise/88988/1 "2022-10-20T02:07:12Z")

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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!

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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:** [October 20, 2022, 4:37am UTC](https://discourse.julialang.org/t/how-to-integrate-a-multi-dimensional-sde-forced-by-the-same-source-of-noise/88988/2 "2022-10-20T04:37:45Z")

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