11 citations · 26 across the 6 of their papers we have counts for
7 papers
Quantitative Universal Approximation Bounds for Deep Belief Networks
Julian Sieber, Johann Gehringer
We show that deep belief networks with binary hidden units can approximate any multivariate probability density under very mild integrability requirements on the parental density o…
Functional Limit Theorems for Volterra Processes and Applications to Homogenization
Johann Gehringer, Xue-Mei Li, Julian Sieber
We prove an enhanced limit theorem for additive functionals of a multi-dimensional Volterra process in the rough path topology. As an application, we establish we…
Rough Homogenisation with Fractional Dynamics
Johann Gehringer, Xue-Mei Li
We review recent developments of slow/fast stochastic differential equations, and also present a new result on Diffusion Homogenisation Theory with fractional and non-strong-mixing…
Functional Limit Theorems of moving averages of Hermite processes and an application to homogenization
Johann Gehringer
We aim to generalize the homogenisation theorem in \cite{Gehringer-Li-tagged} for a passive tracer interacting with a fractional Gaußian noise to also cover fractional non-Gaußian…
Diffusive and rough homogenisation in fractional noise field
Johann Gehringer, Xue-Mei Li
With recently developed tools, we prove a homogenisation theorem for a random ODE with short and long-range dependent fractional noise. The effective dynamics are not necessarily d…
Functional limit theorems for the fractional Ornstein-Uhlenbeck process
Johann Gehringer, Xue-Mei Li
We prove a functional limit theorem for vector-valued functionals of the fractional Ornstein-Uhlenbeck process, providing the foundation for the fluctuation theory of slow/fast sys…
Homogenization with fractional random fields
Johann Gehringer, Xue-Mei Li
We consider a system of differential equations in a fast long range dependent random environment and prove a homogenization theorem involving multiple scaling constants. The effect…