  We study a class of multivariate tempered stable distributions and introduce
the associated class of tempered stable Sato subordinators. These Sato
subordinators are used to build additive inhomogeneous processes by
subordination of a multiparameter Brownian motion. The resulting process is
additive and time inhomogeneous. Furthermore, these processes are associated
with the distribution at unit time of a class of L\'evy process with good fit
properties on fifinancial data. The main feature of the Sato subordinated
Brownian motion is that it has time dependent correlation, whereas the L\'evy
counterpart does not. We provide a numerical illustration of the correlation
dynamics.
