Instantaneous blowup for interacting SDEs with superlinear drift

Mathew Joseph; Shubham Ovhal

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arXiv · 2506.21164

Instantaneous blowup for interacting SDEs with superlinear drift

Mathew Joseph·Shubham Ovhal

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Abstract

We consider a system of interacting SDEs on the integer lattice with multiplicative noise and a drift satisfying the finite Osgood's condition. We show instantaneous everywhere blowup for initial profiles decaying slower than $\exp \left( -\sqrt{\big|\log |x|\big|}\right)$. We employ the splitting-up method to compare the interacting system to a one-dimensional SDE which blows up.

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Mathew Joseph, Shubham Ovhal. 2025-06-26. Instantaneous blowup for interacting SDEs with superlinear drift. https://arxiv.org/abs/2506.21164

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