Some confusion in Example 4 in the tutorial for SDE (related to "diagonality") #777
Description
The tutorial for SDE includes the Example 2: Systems of SDEs with Diagonal Noise. I am afraid it is somewhat unclear. It reads that
every variable in the system gets a different random kick. Consequently, g is a diagonal matrix ...
and then the example contains the following code for the g function
function σ_lorenz!(du, u, p, t)
du[1] = 3.0
du[2] = 3.0
du[3] = 3.0
end
This does not seem like a diagonal matrix function. Instead, it appears as if the function g was defined as (column)vector function g() = [3, 3, 3], which would then suggest that just a single random process is considered.
Then there is also the sentence
Consider for example a stochastic variant of the Lorenz equations, where we introduce a simple additive noise to each of x,y,z, which is simply 3*N(0,dt).
Besides the formal issue that no x, y, and z are previously defined in the example (probably they stand for the three components of the vector u of unknowns, but it should be stated explicitly to avoid confusion), this contributes to the confusion about the whole concept of "diagonality", because it does not help dispel the confusion if just a single random variable corresponding to the3*N(0,dt) is generated and added to each component of equation, of if three independent values are going to be randomly generated.