Unbiased Monte Carlo estimation for solving of linear integral equation, with error estimate

TL;DR

This paper introduces an unbiased Monte Carlo method for solving linear integral equations, including those with weak singularities, providing confidence regions and improving estimation accuracy.

Contribution

The paper presents a novel Monte Carlo approach that yields unbiased solutions for Volterra and Fredholm equations, particularly addressing equations with weak singularities.

Findings

Unbiased Monte Carlo estimations for integral equations.

Effective confidence region construction.

Application to Abelian type equations with weak singularity.

Abstract

We offer a new Monte-Carlo method for solving of linear integral equation which gives the unbiased estimation for solution of Volterra's and Fredholm's type, and consider the problem of confidence region building. We study especially the case of the so-called equations with weak singularity in the kernel of Abelian type.