4 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…
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…
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…