Stochastic elliptic operators defined by non-gaussian random fields with uncertain spectrum

TL;DR

This paper develops a framework for stochastic elliptic operators driven by non-Gaussian random fields with uncertain spectra, analyzing their properties and implications for stochastic homogenization in 3D domains.

Contribution

It introduces a novel class of non-Gaussian random fields with uncertain spectral measures and studies their impact on stochastic elliptic boundary value problems.

Findings

Construction of non-Gaussian positive-definite matrix-valued random fields.

Analysis of stochastic elliptic boundary value problems in 3D.

Insights into stochastic homogenization with uncertain spectral measures.

Abstract

This paper present a construction and the analysis of a class of non-Gaussian positive-definite matrix-valued homogeneous random fields with uncertain spectral measure for stochastic elliptic operators. Then the stochastic elliptic boundary value problem in a bounded domain of the 3D-space is introduced and analyzed for stochastic homogenization.