Z. Ergemlidze, A. Shangua, V. Tarieladze

Sample Behavior and Laws of Large Numbers for Gaussian Random Elements

Criteria for almost sure boundedness and convergence to zero almost surely of Banach space valued independent Gaussian random elements are found.  The obtained statements can be viewed as vector-valued versions of the corresponding results due to N. Vakhania. Moreover, from the obtained statements a strong law of large numbers is derived in the form of Yu. V. Prokhorov.