35 citations · 144 across the 25 of their papers we have counts for
39 papers
Non-uniqueness for McKean--Vlasov SDEs with Hölder diffusion coefficients
Martin Bergerhausen, Paul Nikolaev, David J. Prömel
We show that uniqueness may fail for one-dimensional McKean--Vlasov stochastic differential equations with Hölder continuous diffusion coefficients. More precisely, for every \(α\i…
Stability results for distribution-dependent stochastic Volterra equations
Martin Bergerhausen, David J. Prömel
We investigate stability properties of distribution-dependent stochastic Volterra equations with respect to changes in the coefficients, the Volterra kernels, and the initial condi…
Global universality via discrete-time signatures
Mihriban Ceylan, David J. Prömel
We establish global universal approximation theorems for non-anticipative and general path-dependent functionals on spaces of piecewise linear paths, stating that linear functional…
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…
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…
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…
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…
Functional differential equations driven by càdlàg rough paths
Anna P. Kwossek, Andreas Neuenkirch, David J. Prömel
The existence of unique solutions is established for rough differential equations (RDEs) with path-dependent coefficients and driven by càdlàg rough paths. Moreover, it is shown th…
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…
Well-posedness of diffusion-aggregation equations with bounded kernels and their mean-field approximations
Li Chen, Paul Nikolaev, David J. Prömel
The well-posedness and regularity properties of diffusion-aggregation equations, emerging from interacting particle systems, are established on the whole space for bounded interact…
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 càdlà…
Mean-field stochastic Volterra equations
David J. Prömel, David Scheffels
The well-posedness is established for multi-dimensional mean-field stochastic Volterra equations with Lipschitz continuous coefficients and allowing for singular kernels as well as…
Hegselmann--Krause model with environmental noise
Li Chen, Paul Nikolaev, David J. Prömel
We study a continuous-time version of the Hegselmann-Krause model describing the opinion dynamics of interacting agents subject to random perturbations. Mathematically speaking, th…
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 coef…
On the existence of weak solutions to stochastic Volterra equations
David J. Prömel, David Scheffels
The existence of weak solutions is established for stochastic Volterra equations with time-inhomogeneous coefficients allowing for general kernels in the drift and convolutional or…
Stochastic Volterra equations with Hölder diffusion coefficients
David J. Prömel, David Scheffels
The existence of strong solutions and pathwise uniqueness are established for one-dimensional stochastic Volterra equations with locally H{ö}lder continuous diffusion coefficients…
A Càdlàg Rough Path Foundation for Robust Finance
Andrew L. Allan, Chong Liu, David J. Prömel
Using rough path theory, we provide a pathwise foundation for stochastic Itô integration, which covers most commonly applied trading strategies and mathematical models of financial…
Model-free Portfolio Theory: A Rough Path Approach
Andrew L. Allan, Christa Cuchiero, Chong Liu +1
Based on a rough path foundation, we develop a model-free approach to stochastic portfolio theory (SPT). Our approach allows to handle significantly more general portfolios compare…
A Sobolev rough path extension theorem via regularity structures
Chong Liu, David J. Prömel, Josef Teichmann
We show that every -valued Sobolev path with regularity and integrability can be lifted to a Sobolev rough path provided . The novelty of our appr…
One-dimensional game-theoretic differential equations
Rafał M. Łochowski, Nicolas Perkowski, David J. Prömel
We provide a very brief introduction to typical paths and the corresponding Itô type integration. Relying on this robust Itô integration, we prove an existence and uniqueness resul…
Càdlàg Rough Differential Equations with Reflecting Barriers
Andrew L. Allan, Chong Liu, David J. Prömel
We investigate rough differential equations with a time-dependent reflecting lower barrier, where both the driving (rough) path and the barrier itself may have jumps. Assuming the…
Local times and Tanaka--Meyer formulae for càdlàg paths
Rafał M. Łochowski, Jan Obłój, David J. Prömel +1
Three concepts of local times for deterministic c{à}dl{à}g paths are developed and the corresponding pathwise Tanaka--Meyer formulae are provided. For semimartingales, it is shown…
Martingale optimal transport duality
Patrick Cheridito, Matti Kiiski, David J. Prömel +1
We obtain a dual representation of the Kantorovich functional defined for functions on the Skorokhod space using quotient sets. Our representation takes the form of a Choquet capac…
Existence and uniqueness results for time-inhomogeneous time-change equations and Fokker--Planck equations
Leif Döring, Lukas Gonon, David J. Prömel +1
We prove existence and uniqueness of solutions to Fokker--Planck equations associated to Markov operators multiplicatively perturbed by degenerate time-inhomogeneous coefficients.…