  This note provides a simple sufficient condition ensuring that solutions of
stochastic delay differential equations (SDDEs) driven by subordinators are
non-negative. While, to the best of our knowledge, no simple non-negativity
conditions are available in the context of SDDEs, we compare our result to the
literature within the subclass of invertible continuous-time ARMA (CARMA)
processes. In particular, we analyze why our condition cannot be necessary for
CARMA($p,q$) processes when $p=2$, and we show that there are various
situations where our condition applies while existing results do not as soon as
$p\geq 3$. Finally, we extend the result to a multidimensional setting.
