Sub-Gaussian processes and convergence of random series in functional spaces

Abstract

the random process which can be presented by this series can be chosen to be continuous with probability one. The Hunt condition, besides being simple, is also interesting in that it is invariant with respect to the form of the distribution of random variables }k and is formulated in terms of second moments. However, the Hunt method makes essential use of the properties of function exp {i~kt } and does not admit transition to the genera[ case of series ~ ~. hqD~ (t), where q~k(t), k _> 1, are continuous functions while the }.k are the same as in ~}he c~k~ .