6 papers · 1 filter
Weak solutions to distribution-dependent stochastic Volterra equations
Martin Bergerhausen, David J. Prömel
We prove the existence of weak solutions for distribution-dependent stochastic Volterra equations under linear growth and continuity conditions on the coefficients and mild regular…
Stochastic differential equations driven by fractional Brownian motion: dependence on the Hurst parameter
Anna P. Kwossek, Andreas Neuenkirch, David J. Prömel
Stochastic models with fractional Brownian motion as source of randomness have become popular since the early 2000s. Fractional Brownian motion (fBm) is a Gaussian process, whose c…
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…
A rough path approach to pathwise stochastic integration à la Föllmer
Purba Das, Anna P. Kwossek, David J. Prömel
We develop a general framework for pathwise stochastic integration that extends Föllmer's classical approach beyond gradient-type integrands and standard left-point Riemann sums a…
Functional differential equations driven by cà dlà g 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 cà dlà g rough paths. Moreover, it is shown…
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…