# Custom Noise Process for DifferentialEquations.jl
**URL:** https://discourse.julialang.org/t/custom-noise-process-for-differentialequations-jl/111418
**Category:** Modelling & Simulations
**Tags:** question, diffeq
**Created:** [March 10, 2024, 11:17am UTC](https://discourse.julialang.org/t/custom-noise-process-for-differentialequations-jl/111418 "2024-03-10T11:17:52Z")
**Posts on this page:** 3
**Page:** 1
### Author:  [@StefanPerko](https://discourse.julialang.org/u/StefanPerko)
#### Post date: [March 10, 2024, 11:17am UTC](https://discourse.julialang.org/t/custom-noise-process-for-differentialequations-jl/111418/1 "2024-03-10T11:17:52Z")
I’m trying to define my own noise process for usage with the SDEProblem function.
Mathematically its defined like this: take a Brownian motion on [0,1]. Stick the path on [0,1] at its own tail (continuously) to get a process on [0,2]. Keep repeating this to get a process on [0, epochs], where epochs is an integer.
One way to generate a path of this process is to choose a grid size dt and then generate (and save) the increments for the first epoch ([0,1]) and reuse them.
I can define this using NoiseGrid in dimension 1, like this:
```julia
epochs = 2^4
dt = 1/2^7
increments = [sqrt(dt) * randn() for i in 1:Int(1/dt)]
ssbm_values = cumsum([0; repeat(increments, epochs)])
X = NoiseGrid(0:dt:epochs, ssbm_values)
```
I can plot the path like this:
```julia
b(u, p, t) = 0
σ(u, p, t) = 1
prob = SDEProblem(b, σ, 0, (0.0, epochs), noise = X)
sol = solve(prob, EM(), dt = dt)
plot(sol)
```
Now I want to do it in higher dimensions. After some tinkering the following code runs:
```julia
epochs = 2^4
dt = 1/2^10
increments = sqrt(dt) * randn(d, Int(1/dt))
ssbm_values = cumsum(hcat(zeros(d), transpose(repeat(transpose(increments), epochs))), dims = 2)
X = NoiseGrid(0:dt:epochs, [ssbm_values[i,:] for i in 1:size(ssbm_values,1)])
```
However, the following throws a “BoundsError” only when using X as the noise in SDEProblem:
```julia
function b(du, u, p, t)
du = zeros(2)
end
function σ(du, u, p, t)
du[1] = 1.0
du[2] = 1.0
end
prob = SDEProblem(b, σ, zeros(2), (0.0, epochs), noise = X)
sol = solve(prob, EM(), dt = 1/2^10)
```
How do I need to define X to make this work?
(Note that there is potentially a more elegant solution which I have no clue how to make work either: draw a standard Gaussian N, take an independent Brownian Bridge B from 0 to 0. Then define X\_t = B\_{\{t\}} + t N.)
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [March 10, 2024, 11:10pm UTC](https://discourse.julialang.org/t/custom-noise-process-for-differentialequations-jl/111418/2 "2024-03-10T23:10:40Z")
If it’s a scalar noise process then it should be an array of scalars. Otherwise you have a diagonal noise definition so you need an array of length two vectors.
---
### Author:  [@StefanPerko](https://discourse.julialang.org/u/StefanPerko)
#### Post date: [March 11, 2024, 10:03am UTC](https://discourse.julialang.org/t/custom-noise-process-for-differentialequations-jl/111418/3 "2024-03-11T10:03:34Z")
Ahhh, thank you for the tip. I didn’t even question that line because it ran without errors. But the increments/dimensions were arranged the wrong way. The correct line is actually:
```julia
X = NoiseGrid(0:dt:epochs, [ssbm_values[:,i] for i in 1:size(ssbm_values)[2]])
```
and then everything works 🙂