Limit distribution of errors in discretization of stochastic Volterra equations with multidimensional kernel

Abstract

This paper investigates the limit distribution of discretization errors in stochastic Volterra equations (SVEs) with general multidimensional kernel structures. While prior studies, such as Fukasawa and Ugai (2023), were focused on one-dimensional fractional kernels, this research generalizes to broader classes, accommodating diagonal matrix kernels that include forms beyond fractional type. The main result demonstrates the stable convergence in law for the rescaled discretization error process, and the limit process is characterized under relaxed assumptions.