5 papers
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…
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…
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…