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 cyspera cream where to buy provides a simple sufficient condition ensuring that solutions 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 here condition applies while existing results do not as soon as $pge 3$.Finally, we extend the result to a multidimensional setting.