The usual statement of a Hoeffding bound (e.g. https://sites.math.washington.edu/~morrow/335_17/ineq.pdf) requires independent random variables.
My question is: Do there exist bounds similar to Hoeffding's that apply in the case that, for Bernoulli R.V. $X_i$ for $i \in [n]$
$\Pr\left[\bigcap_{i}X_i\right] = \left(\prod_i \Pr[X_i]\right) + \delta$ for $\delta << 1$, maybe specifically for the case that $\delta$ is a negligible function on $n$?
Thanks.