Error Distribution Of The Euler Approximation Scheme For Stochastic Volterra Integral Equations

TL;DR

This paper analyzes the distributional convergence of the normalized error in Euler approximations for stochastic Volterra equations with specific kernels, providing theoretical insights into their accuracy.

Contribution

It establishes the convergence in distribution of the normalized error for Euler schemes applied to stochastic Volterra equations with power-law kernels.

Findings

Normalized error converges in distribution

Provides theoretical foundation for Euler approximation accuracy

Applicable to kernels with b1bd power-law form

Abstract

The purpose of this paper is to establish the convergence in distribution of the normalized error in the Euler approximation scheme for stochastic Volterra equations driven by a standard Brownian motion, with a kernel of the form $(t-s)^\alpha$, where $\alpha \in (-\frac 12, \frac 12)$.