发表机构
The University of Manchester; École Polytechnique Fédérale de Lausanne（曼彻斯特大学; 洛桑联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对具有局部Lipschitz系数的随机微分方程，扩展了动态低秩逼近框架，并证明了其存在性，为高维问题提供高效数值模拟方法。
AI 中文摘要
高维随机微分方程（SDEs）的数值模拟在实际应用中日益广泛，但其计算时间和内存开销可能难以承受。一种可能的解决方案是采用降阶方法（ROMs），在处理低秩问题时能够提供快速且高精度的模拟。在随机微分方程的背景下，动态低秩逼近（DLRA）已在逼近效果和计算效率方面展现出显著成果，因其完全“即时”计算而节省计算时间。本文扩展了我们前期工作arXiv:2308.11581中提出的用于随机微分方程的DLRA框架，通过考虑具有线性增长界的局部Lipschitz漂移和扩散项，证明了该设置下DLRA的存在性。
英文摘要
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.
Comments18 pages
