gpLib.FractionalGaussianNoise

class gpLib.FractionalGaussianNoise(H_prior: Prior | None = None, H_constraint: Interval | None = None, **kwargs)

Discrete fractional Gaussian noise kernel.

For increment lag \(h = x - x'\)

\[k(h) \;=\; \tfrac12 \Bigl(|h+1|^{\alpha} - 2|h|^{\alpha} + |h-1|^{\alpha}\Bigr), \qquad \alpha = 2H,\; H\in(0.5,1).\]

Parameters:

• H_prior – Optional prior on the Hurst index \(H\).

• H_constraint – Interval \((0.51,0.99)\) by default.

Variables:

H (torch.Tensor) – Hurst exponent.