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arXiv · 2609.20307

Existence of Dynamical Low-Rank Approximation for SDEs with Locally Lipschitz Coefficients

Yoshihito Kazashi·Fabio Nobile·Fabio Zoccolan
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Abstract

Numerical simulations of high-dimensional stochastic differential equations (SDEs), which are increasingly employed in real-world applications, can be unaffordable in terms of computational time and memory. A possible solution is the deployment of reduced order methods (ROMs) that provide fast simulations with good accuracy when dealing with low-rank problems. In the context of SDEs, the Dynamical Low-Rank Approximation (DLRA) already showed remarkable results, in terms of approximation and computational efficiency of computational time because of being completely computed "on-the-fly". In this article, we extend the framework of DLRA for SDEs proposed in our primary work arXiv:2308.11581 by considering locally Lipschitz drift and diffusion with linear-growth bound, by showing the existence of DLRA for this setting.

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Yoshihito Kazashi, Fabio Nobile, Fabio Zoccolan. 2026-09-20. Existence of Dynamical Low-Rank Approximation for SDEs with Locally Lipschitz Coefficients. https://arxiv.org/abs/2609.20307

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