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Existence of Dynamical Low-Rank Approximation for SDEs with Locally Lipschitz Coefficients
Abstract
In this work, we consider the Dynamical Low Rank Approximation (DLRA) of a high-dimensional system of Stochastic Differential Equations (SDEs); DLRA is an effective reduced order model that projects the equations on a time-varying low dimensional subspace following the evolution of the solution. Well posedness results for the resulting DLRA equations have been proved in arXiv:2308.11581 under the assumption of global Lipschitz continuity and linear growth of the drift and the diffusion coefficients. In this work, we extend the existence result to the case of locally Lipschitz coefficient and we prove uniqueness of solutions under the assumption of a mild growth of the Lipschitz constant to infinity.
Related
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BibTeX
@misc{kazashi2026existence,
title = {{Existence of Dynamical Low-Rank Approximation for SDEs with Locally Lipschitz Coefficients}},
author = {Yoshihito Kazashi and Fabio Nobile and Fabio Zoccolan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.20307},
eprint = {2609.20307},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20307},
}
RIS
TY - UNPB
TI - Existence of Dynamical Low-Rank Approximation for SDEs with Locally Lipschitz Coefficients
AU - Yoshihito Kazashi
AU - Fabio Nobile
AU - Fabio Zoccolan
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2609.20307
UR - https://arxiv.org/abs/2609.20307
AB - In this work, we consider the Dynamical Low Rank Approximation (DLRA) of a high-dimensional system of Stochastic Differential Equations (SDEs); DLRA is an effective reduced order model that projects the equations on a time-varying low dimensional subspace following the evolution of the solution. Well posedness results for the resulting DLRA equations have been proved in arXiv:2308.11581 under the assumption of global Lipschitz continuity and linear growth of the drift and the diffusion coefficients. In this work, we extend the existence result to the case of locally Lipschitz coefficient and we prove uniqueness of solutions under the assumption of a mild growth of the Lipschitz constant to infinity.
ER -