MATHICSE-GroupKazashi, YoshihitoNobile, Fabio2020-02-072020-02-072020-02-072020-02-0610.5075/epfl-MATHICSE-274320https://infoscience.epfl.ch/handle/20.500.14299/165200An existence result is presented for the dynamical low rank (DLR) approximation for random semi-linear evolutionary equations. The DLR solution approximates the true solution at each time instant by a linear combination of products of deterministic and stochastic basis functions, both of which evolve over time. A key to our proof is to find a suitable equivalent formulation of the original problem. The so-called Dual Dynamically Orthogonal formulation turns out to be convenient. Based on this formulation, the DLR approximation is recast to an abstract Cauchy problem in a suitable linear space, for which existence and uniqueness of the solution in the maximal interval are established.text::working paper