1D stochastic pressure equation with log-correlated Gaussian coefficients
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.
Authors
- Eero Saksman (ORCID: https://orcid.org/0000-0002-7630-7135)
- Lauri Viitasaari (ORCID: https://orcid.org/0000-0002-3015-8664)
- Jonas M. Tölle (ORCID: https://orcid.org/0000-0002-6020-4131)
- Benny Avelin (ORCID: https://orcid.org/0000-0002-1429-4965)
- Patrik Nummi (ORCID: https://orcid.org/0000-0002-3480-4627)
- Tuomo Kuusi
Institutions
- Uppsala University (SE)
- Helsinki Institute of Physics (FI)
- Aalto University (FI)
Publication Details
- Journal
- Stochastic Processes and their Applications
- Published
- 2025-10-23
- DOI
- https://doi.org/10.1016/j.spa.2025.104808
- Primary Topic
- Stochastic processes and financial applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00