gpLib.fBMKernel

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

Fractional Brownian motion covariance

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

The kernel is non-stationary and self-similar of order \(H\).

Parameters:

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

Variables:

H (torch.Tensor) – Hurst exponent.