35 citations · 144 across the 25 of their papers we have counts for
29 papers · 1 filter
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…
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…
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…
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…
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.…
Paracontrolled distribution approach to stochastic Volterra equations
David J. Prömel, Mathias Trabs
Based on the notion of paracontrolled distributions, we provide existence and uniqueness results for rough Volterra equations of convolution type with potentially singular kernels…
Examples of Itô càdlàg rough paths
Chong Liu, David J. Prömel
Based on a dyadic approximation of Itô integrals, we show the existence of Itô càdlàg rough paths above general semimartingales, suitable Gaussian processes and non-negative typica…
On Skorokhod Embeddings and Poisson Equations
Leif Doering, Lukas Gonon, David J. Prömel +1
The classical Skorokhod embedding problem for a Brownian motion asks to find a stopping time so that is distributed according to a prescribed probability distribution…
Stochastic Analysis with Modelled Distributions
Chong Liu, David J. Prömel, Josef Teichmann
Using a Besov topology on spaces of modelled distributions in the framework of Hairer's regularity structures, we prove the reconstruction theorem on these Besov spaces with negati…
Rough path metrics on a Besov--Nikolskii type scale
Peter K. Friz, David J. Prömel
It is known, since the seminal work [T. Lyons, Differential equations driven by rough signals, Rev. Mat. Iberoamericana, 14 (1998)], that the solution map associated to a controlle…