Abstract

Tempered fractional Brownian motion and tempered fractional Brownian motion of the second kind modify the power-law kernel in the moving average representation of fractional Brownian motion by introducing an exponential tempering. We construct least-square estimators for the unknown drift parameters within Vasicek models that are driven by these processes. To demonstrate their strong consistency, we establish asymptotic bounds with probability 1 for the rate of growth of trajectories of tempered fractional processes.