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- W4386114413 abstract "In this paper, we set the mathematical foundations of the Dynamical Low Rank Approximation (DLRA) method for high-dimensional stochastic differential equations. DLRA aims at approximating the solution as a linear combination of a small number of basis vectors with random coefficients (low rank format) with the peculiarity that both the basis vectors and the random coefficients vary in time. While the formulation and properties of DLRA are now well understood for random/parametric equations, the same cannot be said for SDEs and this work aims to fill this gap. We start by rigorously formulating a Dynamically Orthogonal (DO) approximation (an instance of DLRA successfully used in applications) for SDEs, which we then generalize to define a parametrization independent DLRA for SDEs. We show local well-posedness of the DO equations and their equivalence with the DLRA formulation. We also characterize the explosion time of the DO solution by a loss of linear independence of the random coefficients defining the solution expansion and give sufficient conditions for global existence." @default.
- W4386114413 created "2023-08-24" @default.
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- W4386114413 date "2023-08-22" @default.
- W4386114413 modified "2023-09-27" @default.
- W4386114413 title "Dynamically Orthogonal Approximation for Stochastic Differential Equations" @default.
- W4386114413 doi "https://doi.org/10.48550/arxiv.2308.11581" @default.
- W4386114413 hasPublicationYear "2023" @default.
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