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math.PR2023
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…
math.PR2023
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…
math.PR2023
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…