A central limit theorem for the Euler integral of a Gaussian random field

TL;DR

This paper establishes a central limit theorem for the Euler integral of Gaussian noise fields, providing foundational statistical insights crucial for applications involving noisy data in signal processing and network sensing.

Contribution

It introduces the first asymptotic distribution result, a central limit theorem, for the Euler integral of Gaussian noise fields, advancing the statistical understanding of these integrals.

Findings

Proves a central limit theorem for the Euler integral of Gaussian noise fields

Provides a basis for statistical analysis of noisy data in applications

Enhances understanding of asymptotic behavior of Euler integrals in stochastic settings

Abstract

Euler integrals of deterministic functions have recently been shown to have a wide variety of possible applications, including in signal processing, data aggregation and network sensing. Adding random noise to these scenarios, as is natural in the majority of applications, leads to a need for statistical analysis, the first step of which requires asymptotic distribution results for estimators. The first such result is provided in this paper, as a central limit theorem for the Euler integral of pure, Gaussian, noise fields.