Z. Ergemlidze, A. Shangua, V. Tarieladze

Sample Behavior and Laws of Large Numbers for Gaussian Random Elements

abstract:
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.