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1D stochastic pressure equation with log-correlated Gaussian coefficients

Author

Listed:
  • Avelin, Benny
  • Kuusi, Tuomo
  • Nummi, Patrik
  • Saksman, Eero
  • Tölle, Jonas M.
  • Viitasaari, Lauri

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.

Suggested Citation

  • Avelin, Benny & Kuusi, Tuomo & Nummi, Patrik & Saksman, Eero & Tölle, Jonas M. & Viitasaari, Lauri, 2026. "1D stochastic pressure equation with log-correlated Gaussian coefficients," Stochastic Processes and their Applications, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:spapps:v:192:y:2026:i:c:s0304414925002522
    DOI: 10.1016/j.spa.2025.104808
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    References listed on IDEAS

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    1. Li, Dingshi & Fan, Xiaoming, 2017. "Exponential stability of impulsive stochastic partial differential equations with delays," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 185-192.
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