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

2024/12/17 by Busse, Julius
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2412.13383

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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