6 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…
Neural stochastic Volterra equations: learning path-dependent dynamics
Martin Bergerhausen, David J. Prömel, David Scheffels
Stochastic Volterra equations (SVEs) serve as mathematical models for the time evolutions of random systems with memory effects and irregular behaviour. We introduce neural stochas…
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…
Pathwise convergence of the Euler scheme for rough and stochastic differential equations
Andrew L. Allan, Anna P. Kwossek, Chong Liu +1
The convergence of the first order Euler scheme and an approximative variant thereof, along with convergence rates, are established for rough differential equations driven by cà dl…
Universal approximation property of neural stochastic differential equations
Anna P. Kwossek, David J. Prömel, Josef Teichmann
We identify various classes of neural networks that are able to approximate continuous functions locally uniformly subject to fixed global linear growth constraints. For such neura…
Characterization of Besov spaces with dominating mixed smoothness by differences
Paul Nikolaev, David J. Prömel, Mathias Trabs
Besov spaces with dominating mixed smoothness, on the product of the real line and the torus as well as bounded domains, are studied. A characterization of these function spaces in…