DOAJ
Open Access
2021
On nonnegative solutions of SDDEs with an application to CARMA processes
Mikkel Slot Nielsen
Victor Rohde
Abstrak
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.
Topik & Kata Kunci
Penulis (2)
M
Mikkel Slot Nielsen
V
Victor Rohde
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2021
- Sumber Database
- DOAJ
- DOI
- 10.15559/21-VMSTA177
- Akses
- Open Access ✓