Strong completeness of SDEs and non-explosion for RDEs with coefficients having unbounded derivatives
Probability
2026-01-27 v3 Classical Analysis and ODEs
Abstract
We establish a non-explosion result for rough differential equations (RDEs) in which the noise and drift coefficients, together with their derivatives, may grow unboundedly at infinity. In addition, we prove the existence of a global bi-continuous solution flow for stochastic differential equations (SDEs). Finally, the non-explosion results for RDEs are shown to be sharp by constructing counterexamples.
Keywords
Cite
@article{arxiv.2502.08799,
title = {Strong completeness of SDEs and non-explosion for RDEs with coefficients having unbounded derivatives},
author = {Xue-Mei Li and Kexing Ying},
journal= {arXiv preprint arXiv:2502.08799},
year = {2026}
}
Comments
Accepted version, to appear in The Annals of Probability