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This is a Quantitative Study study.

October 16, 2025Open Access

Instantaneous blowup for interacting SDEs with superlinear drift

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The study shows that a system of interacting SDEs can exhibit instantaneous blowup under specific conditions.
A constant initial profile leads to blowup for the drift satisfying the finite Osgood's condition.
The research employs a comparison approach with a one-dimensional SDE to demonstrate this phenomenon.
Findings imply that drift and noise interplay critically in determining system behavior over time.

Implication

Analysis reveals instantaneous blowup in a system of interacting SDEs with multiplicative noise, highlighting drift dynamics.

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 the instantaneous everywhere blowup for the constant initial profile. We employ the splitting-up method to compare the interacting system to a one-dimensional SDE which blows up.

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Cite This Study

Joseph et al. (2025) studied this question.

synapsesocial.com/papers/68f04acce559138a1a06e7a2 https://doi.org/10.48550/arxiv.2506.21164

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Implication

Analysis reveals instantaneous blowup in a system of interacting SDEs with multiplicative noise, highlighting drift dynamics.

Instantaneous blowup for interacting SDEs with superlinear drift

Key Points

Implication

Abstract

Discussion

Cite This Study

Instantaneous blowup for interacting SDEs with superlinear drift

Key Points

Implication

Abstract

Discussion

Cite This Study

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