1D stochastic pressure equation with log-correlated Gaussian coefficients

Benny Avelin, Tuomo Kuusi, Patrik Nummi, Eero Saksman, Jonas M. Tölle and Lauri Viitasaari

Stochastic Processes and their Applications, 2026, vol. 192, issue C

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 S-transform and the Gaussian multiplicative chaos measure.

Keywords: Stochastic boundary value problems; Elliptic second order random ordinary differential equations; Gaussian log-correlated fields; Gaussian multiplicative chaos; Wick products; Renormalization; Hida–Kondratiev distributions; S-transform (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1016/j.spa.2025.104808

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