Tempered fractional Brownian motion

Tempered fractional Brownian motion (TFBM) modifies the power law kernel in the moving average representation of a fractional Brownian motion, adding an exponential tempering. Tempered fractional Gaussian noise (TFGN), the increments of TFBM, form a stationary time series that can exhibit semi-long range dependence. This paper develops the basic theory of TFBM, including moving average and spectral representations, sample path properties, and an application to modeling wind speed.