On nonnegative solutions of SDDEs with an application to CARMA processes

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