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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.13383 |
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| _version_ | 1866913616619372544 |
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| author | Busse, Julius |
| author_facet | Busse, Julius |
| contents | Motivated by a recent publication by Ishiwata and Nakata (2022), we prove that sufficiently regular stochastic delay differential equations (SDDEs) with a single discrete delay have blow up solutions if and only if their undelayed counterparts have them, using a comparison theorem by Ikeda and Watanabe (1977). This result has applications in mathematical biology and finance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13383 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic Delay Differential Equations have blow-up solutions if and only if their instantaneous counterparts have them Busse, Julius Probability Motivated by a recent publication by Ishiwata and Nakata (2022), we prove that sufficiently regular stochastic delay differential equations (SDDEs) with a single discrete delay have blow up solutions if and only if their undelayed counterparts have them, using a comparison theorem by Ikeda and Watanabe (1977). This result has applications in mathematical biology and finance. |
| title | Stochastic Delay Differential Equations have blow-up solutions if and only if their instantaneous counterparts have them |
| topic | Probability |
| url | https://arxiv.org/abs/2412.13383 |