pr.probability – Random Fourier series in Hilbert space

Let $H$ be a Hilbert space, and $X_n$,
$ nin mathbb {Z}$, be a sequence of independent Bernoulli random variables
$P(X_n = pm 1) = frac 12$. Is there a characterization of the sequences
$a_n$, $ nin mathbb{Z}$, in $H$ such that the series
$$
sum_n a_n X_n e^{int}, quad t in (0,2pi),
$$

is almost surely uniformly convergent in $H$?