1D stochastic pressure equation with log-correlated Gaussian coefficients
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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en
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23
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Stochastic Processes and their Applications, Volume 192, pp. 1-23
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.Description
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Avelin, B, Kuusi, T, Nummi, P, Saksman, E, Tölle, J M & Viitasaari, L 2026, '1D stochastic pressure equation with log-correlated Gaussian coefficients', Stochastic Processes and their Applications, vol. 192, 104808, pp. 1-23. https://doi.org/10.1016/j.spa.2025.104808