# Non-diagonal noise correlation matrix

**URL:** https://discourse.julialang.org/t/non-diagonal-noise-correlation-matrix/57393
**Category:** New to Julia
**Created:** [March 17, 2021, 3:55pm UTC](https://discourse.julialang.org/t/non-diagonal-noise-correlation-matrix/57393 "2021-03-17T15:55:05Z")
**Posts on this page:** 1
**Page:** 1

<div class="post-metadata">

### Author: ![Amir\_Abbasi](https://avatars.discourse-cdn.com/v4/letter/a/9d8465/32.png) [@Amir\_Abbasi](https://discourse.julialang.org/u/Amir_Abbasi)
#### Post date: [March 17, 2021, 3:55pm UTC](https://discourse.julialang.org/t/non-diagonal-noise-correlation-matrix/57393/1 "2021-03-17T15:55:05Z")

</div>

Hi all!

I am newbie to julia and I am playing with it to solve SDE systems, numerically.  
I had a look at Non-diagonal noise Tutorial (Example No. 4) [https://diffeq.sciml.ai/stable/tutorials/sde\_example/](https://diffeq.sciml.ai/stable/tutorials/sde_example/), but still something is not clear for me which I explain below:

Lets assume that we have two coupled SDEs

dx1 = a11_x1_dt + a12_x2_dt + dw1  
dx2 = a21_x1_dt + a22_x2_dt + dw2  
a\_ij’s here are all state dependent. dw1 and dw2 have Non-diagonal, state dependent (x1 and x2 dependent) cross-correlation so that we can generally say:

dw\_i\*dw\_i = b\_ij dt

where b\_ij is the element-wise representation of noise correlation matrix:

How should one solve this sort of problem using non-diagonal noise option in julia?  
Which solver is recommended?