fbm_msd: Mean square displacement of fractional Brownian motion.

In SuperGauss: Superfast Likelihood Inference for Stationary Gaussian Time Series

Mean square displacement of fractional Brownian motion.

Description

Mean square displacement of fractional Brownian motion.

Usage

fbm_msd(tseq, H)

Arguments

tseq	Length-N vector of timepoints.
H	Hurst parameter (between 0 and 1).

Details

The mean squared displacement (MSD) of a stochastic process X_t is defined as

MSD(t) = E[(X_t - X_0)^2].

Fractional Brownian motion (fBM) is a continuous Gaussian process with stationary increments, such that its covariance function is entirely defined the MSD, which in this case is ⁠MSD(t) = |t|^(2H)⁠.

Value

Length-N vector of mean square displacements.

Examples

fbm_msd(tseq = 1:10, H = 0.4)

SuperGauss documentation built on Sept. 10, 2025, 10:32 a.m.