Fractional Brownian motion with negative Hurst exponent (opens in new tab)

Fractional Brownian motion (fBm) is an important scale-invariant Gaussian non-Markovian process with stationary increments, which serves as a prototypical example of a system with long-range temporal correlations and anomalous diffusion. The fBm is traditionally defined for the Hurst exponent in the range . Here we extend this definition to the regime . The extended fBm is not a pointwise process, so we regularize it via a local temporal averaging with a narrow kernel. The resulting process i...