Stochastic Delay Differential Equations have blow-up solutions if and only if their instantaneous counterparts have them

Julius Busse

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arXiv · 2412.13383

Stochastic Delay Differential Equations have blow-up solutions if and only if their instantaneous counterparts have them

Julius Busse

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Abstract

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.

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Julius Busse. 2024-12-17. Stochastic Delay Differential Equations have blow-up solutions if and only if their instantaneous counterparts have them. https://arxiv.org/abs/2412.13383

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