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

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. MSC classes: 58J65, 60H10, 60H35, 65C30