On nonnegative solutions of SDDEs with an application to CARMA processes

On nonnegative solutions of SDDEs with an application to CARMA processes

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This note provides a simple sufficient condition ensuring that solutions redken shades 9gi of stochastic delay differential equations (SDDEs) driven by subordinators are nonnegative.While, to the best of our knowledge, no simple nonnegativity 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 animed blue lotion topical spray as soon as $pge 3$.Finally, we extend the result to a multidimensional setting.