The aim of this intership in the study of stress fluctuations in materials for comprehending their elastic and transport properties. It focuses on the Hebraud-Lequeux (HL) model, a phenomenological approach that describes the rheological behavior of soft glassy materials. The HL model relies on a distribution function that evolves over time due to external stress, incorporating both elastic and viscous forces, as well as thermal fluctuations. A fundamental issue is the deduction of macroscopic phenomena from microscopic dynamics. The internship's objective is to formulate a microscopic theory describing stress fluctuations in materials, starting with a simplified system of Brownian particles. The aim is to gain a deeper understanding of the microscopic processes that give rise to macroscopic stress fluctuations, which can then be applied to investigate the viscoelastic and transport properties of complex materials.