论文标题
SDDE的非负解决方案，并应用于CARMA流程
On non-negative solutions of SDDEs with an application to CARMA processes
论文作者
论文摘要
本说明提供了一个简单的条件，确保了下属驱动的随机延迟微分方程（SDDE）的解决方案是非负数的。据我们所知，在SDDE的背景下没有简单的非负条件，我们将结果与可逆连续时间ARMA（CARMA）过程中的文献进行了比较。特别是，我们分析了为什么当$ p = 2 $时，Carma（$ P，Q $）流程不需要我们的病情，并且我们表明在各种情况下，我们的病情适用，而现有结果并不是$ P \ geq 3 $。最后，我们将结果扩展到多维设置。
This note provides a simple sufficient condition ensuring that solutions of stochastic delay differential equations (SDDEs) driven by subordinators are non-negative. While, to the best of our knowledge, no simple non-negativity conditions are available in the context of SDDEs, we compare our result to the literature within the subclass of invertible continuous-time ARMA (CARMA) processes. In particular, we analyze why our condition cannot be necessary for CARMA($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.
