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

On non-negative solutions of SDDEs with an application to CARMA processes