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Strong solutions of SDEs with critical discontinuities in diffusion coefficients
Abstract
We prove strong existence for Itô SDEs with diffusion coefficients that can introduce strong attraction to a submanifold. We extend and strengthen the Röckner-Zhao approach, which uses Malliavin calculus to establish compactness of the approximating solutions in Wiener-Sobolev space. At least when the diffusion coefficients are sufficiently regular in time, this provides an alternative to Krylov's recent proof of strong existence via analysis of the Itô-Duhamel series.
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BibTeX
@misc{boutiah2026strong,
title = {{Strong solutions of SDEs with critical discontinuities in diffusion coefficients}},
author = {S. E. Boutiah and D. Kinzebulatov},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28528},
eprint = {2608.28528},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28528},
}
RIS
TY - UNPB
TI - Strong solutions of SDEs with critical discontinuities in diffusion coefficients
AU - S. E. Boutiah
AU - D. Kinzebulatov
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28528
UR - https://arxiv.org/abs/2608.28528
AB - We prove strong existence for Itô SDEs with diffusion coefficients that can introduce strong attraction to a submanifold. We extend and strengthen the Röckner-Zhao approach, which uses Malliavin calculus to establish compactness of the approximating solutions in Wiener-Sobolev space. At least when the diffusion coefficients are sufficiently regular in time, this provides an alternative to Krylov's recent proof of strong existence via analysis of the Itô-Duhamel series.
ER -