Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On non-negative solutions of SDDEs with an application to CARMA
  processes   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.

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The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th