Central limit theorem of Multilevel Monte Carlo Euler estimators for Stochastic Volterra equations with fractional kernels

TL;DR

This paper establishes a central limit theorem for multilevel Monte Carlo Euler estimators applied to stochastic Volterra equations with fractional kernels, advancing the theoretical understanding of their statistical properties.

Contribution

It proves a Lindeberg-Feller type central limit theorem for these estimators, which was previously unestablished for this class of equations.

Findings

Central limit theorem proven for the estimators

Theoretical foundation for statistical analysis of stochastic Volterra equations

Enhanced understanding of Monte Carlo methods for fractional kernels

Abstract

This paper is devoted to proving a (Lindeberg-Feller type ) central limit theorem for the multilevel Monte Carlo estimator associated with the Euler discretization scheme for the stochastic Volterra equations with fractional kernels $K(u)=u^{H-\frac{1}{2}}/\Gamma(H+1/2), H\in (0,1/2]$.