  In the last decade the subordinated processes have become popular and found
many practical applications. Therefore in this paper we examine two processes
related to time-changed (subordinated) classical Brownian motion with drift
(called arithmetic Brownian motion). The first one, so called normal tempered
stable, is related to the tempered stable subordinator, while the second one -
to the inverse tempered stable process. We compare the main properties (such as
probability density functions, Laplace transforms, ensemble averaged mean
squared displacements) of such two subordinated processes and propose the
parameters' estimation procedures. Moreover we calibrate the analyzed systems
to real data related to indoor air quality.
