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...
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| creator | Nielsen, Mikkel Slot Rohde, Victor |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.2010.08284 |
| format | Article |
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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.</description><identifier>DOI: 10.48550/arxiv.2010.08284</identifier><language>eng</language><subject>Mathematics - Probability</subject><creationdate>2020-10</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2010.08284$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2010.08284$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Nielsen, Mikkel Slot</creatorcontrib><creatorcontrib>Rohde, Victor</creatorcontrib><title>On non-negative solutions of SDDEs with an application to CARMA processes</title><description>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.</description><subject>Mathematics - Probability</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj8FOwzAQRH3hgAofwIn9gRTH3trOMUoLVCqqBL1HjusFS8GO4lDg72lLTzOaJ430GLsr-RzNYsEf7PgTDnPBjwM3wuA1W28jxBSL6N_tFA4ecuq_ppBihkTwtlyuMnyH6QNsBDsMfXD2RGFK0NSvLzUMY3I-Z59v2BXZPvvbS87Y7nG1a56LzfZp3dSbwiqNhfedKvcGnSDlaU9WmRKFVth1iFxWiouq0kSkj0U5zklyL9AYp6WkTssZu_-_Pbu0wxg-7fjbnpzas5P8A2GlRdY</recordid><startdate>20201016</startdate><enddate>20201016</enddate><creator>Nielsen, Mikkel Slot</creator><creator>Rohde, Victor</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20201016</creationdate><title>On non-negative solutions of SDDEs with an application to CARMA processes</title><author>Nielsen, Mikkel Slot ; Rohde, Victor</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a674-eeb61d84c2f6efdfa68142764bb44039602997fff70296c00f30e2488c733fb73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Mathematics - Probability</topic><toplevel>online_resources</toplevel><creatorcontrib>Nielsen, Mikkel Slot</creatorcontrib><creatorcontrib>Rohde, Victor</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Nielsen, Mikkel Slot</au><au>Rohde, Victor</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On non-negative solutions of SDDEs with an application to CARMA processes</atitle><date>2020-10-16</date><risdate>2020</risdate><abstract>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.</abstract><doi>10.48550/arxiv.2010.08284</doi><oa>free_for_read</oa></addata></record> |
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| title | On non-negative solutions of SDDEs with an application to CARMA processes |
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