4 papers
Global universal approximation with Brownian signatures
Mihriban Ceylan, David J. Prömel
We establish -universal approximation theorems for general path-dependent and non-anticipative functionals on suitable rough path spaces, showing that linear functionals actin…
Global universality via discrete-time signatures
Mihriban Ceylan, David J. Prömel
We establish global universal approximation theorems on spaces of piecewise linear paths, stating that linear functionals of the corresponding signatures are dense with respect to…
Universal approximation with signatures of non-geometric rough paths
Mihriban Ceylan, Anna P. Kwossek, David J. Prömel
We establish a universal approximation theorem for signatures of rough paths that are not necessarily weakly geometric. By extending the path with time and its rough path bracket t…
Distributionally robust approximation property of neural networks
Mihriban Ceylan, David J. Prömel
The universal approximation property uniformly with respect to weakly compact families of measures is established for several classes of neural networks. To that end, we prove that…