4 papers · 1 filter
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…
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…
Pathwise uniqueness for singular stochastic Volterra equations with Hölder coefficients
David J. Prömel, David Scheffels
Pathwise uniqueness is established for a class of one-dimensional stochastic Volterra equations driven by Brownian motion with singular kernels and Hölder continuous diffusion coe…