Huge differences between fft and cholesky method on FBM

[ggmirandac]

Hi,

I am trying your software to do some stochastical simulations with the Fractional Brownian Motion implementation. And I see the following issues, or maybe I am wrong. But when I run a code with the following code:

function fOPU(t0, dt, tf,x_0, H; theta = 0.7, mu = 1.5, sigma = 0.06)
	time = t0:dt:tf
	fbm_o = FBM(time, H)
	sample = rand(fbm_o, method=:fft)
	steps = length(time)
	v = zeros(steps,1)
	v[1] = x_0
	for i = 2:steps
		v[i] = v[i-1] + theta * (mu - v[i-1]) * dt + sigma * (sample[i] - sample[i-1])
	end
	return v
end

function bmOUP(t0, dt, tf, x0; theta = 0.7, mu = 1.5, sigma = 0.06)
	time = t0:dt:tf
	steps = length(time)
	
	v = zeros(steps, 1)
	norm = Distributions.Normal(0,1)
	sample = rand(norm, steps)
	v[1] = x0
	for i = 2:steps
		v[i] = v[i-1]+theta*(mu - v[i-1]) * dt + sigma * sample[i] * sqrt(dt)
	end
	return v
end

When the method in the fOPU function is :ftt the results are:

And when the method is :chol the results are:

As you can see in the :ftt method, the fSDE doesn't compares with the brownian motion equivalent even when the Hurst parameter is 0.5. So, this seems to be an issue in this case.

So, as I can see from this implementation, the :ftt shouldn't be suited for fSDE implementations?