1D stochastic pressure equation with log-correlated Gaussian coefficients
Probability
2025-12-02 v2
Abstract
We study unique solvability for one dimensional stochastic pressure equation with diffusion coefficient given by the Wick exponential of log-correlated Gaussian fields. We prove well-posedness for Dirichlet, Neumann and periodic boundary data, and the initial value problem, covering the cases of both the Wick renormalization of the diffusion and of point-wise multiplication. We provide explicit representations for the solutions in both cases, characterized by the -transform and the Gaussian multiplicative chaos measure.
Keywords
Cite
@article{arxiv.2402.09127,
title = {1D stochastic pressure equation with log-correlated Gaussian coefficients},
author = {Benny Avelin and Tuomo Kuusi and Patrik Nummi and Eero Saksman and Jonas M. Tölle and Lauri Viitasaari},
journal= {arXiv preprint arXiv:2402.09127},
year = {2025}
}