English

Instantaneous blowup for interacting SDEs with superlinear drift

Probability 2026-01-21 v2

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(logx)\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.

Keywords

Cite

@article{arxiv.2506.21164,
  title  = {Instantaneous blowup for interacting SDEs with superlinear drift},
  author = {Mathew Joseph and Shubham Ovhal},
  journal= {arXiv preprint arXiv:2506.21164},
  year   = {2026}
}

Comments

Expanded Section 4 to include non-constant initial profiles

R2 v1 2026-07-01T03:34:19.195Z