On nonnegative solutions of SDDEs with an application to CARMA processes
Open Access
- 31 March 2021
- journal article
- research article
- Published by VTeX in Modern Stochastics: Theory and Applications
- Vol. 8 (3), 309-328
- https://doi.org/10.15559/21-vmsta177
Abstract
Publisher: VTeX - Solutions for Science Publishing, Journal: Modern Stochastics - Theory and Applications, Title: On nonnegative solutions of SDDEs with an application to CARMA processes, Authors: Mikkel Slot Nielsen, Victor Rohde , 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 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 as soon as $p\ge 3$. Finally, we extend the result to a multidimensional setting.
Keywords
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