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.

arXiv comment19 pages