2026-04-13T07:18:25Zhttps://recercat.cat/oai/requestoai:recercat.cat:2445/1928872025-12-05T09:59:00Zcom_2072_1057col_2072_478917col_2072_478920
RECERCAT
author
Hinojosa Calleja, Adrián
author
Sanz-Solé, Marta
2023-01-31T17:48:42Z2023-01-31T17:48:42Z2022-01-092023-01-31T17:48:42Z
Consider the linear stochastic biharmonic heat equation on a $d$-dimensional torus ( $d=1,2,3)$, driven by a space-time white noise and with periodic boundary conditions: $$ \left(\frac{\partial}{\partial t}+(-\Delta)^2\right) v(t, x)=\sigma \dot{W}(t, x),(t, x) \in(0, T] \times \mathbb{T}^d, $$ $v(0, x)=v_0(x)$. We find the canonical pseudo-distance corresponding to the random field solution, therefore the precise description of the anisotropies of the process. We see that for $d=2$, they include a $z\left(\log \frac{c}{z}\right)^{1 / 2}$ term. Consider $D$ independent copies of the random field solution to (0.1). Applying the criteria proved in Hinojosa-Calleja and Sanz-Solé (Stoch PDE Anal Comp 2021. https://doi.org/10.1007/s40072-021-001901), we establish upper and lower bounds for the probabilities that the path process hits bounded Borel sets.This yields results on the polarity of sets and on the Hausdorff dimension of the path process.
(c) Springer, 2022 info:eu-repo/semantics/openAccess
Probabilitats
Processos estocàstics
Equacions en derivades parcials
Processos gaussians
Probabilities
Stochastic processes
Partial differential equations
Gaussian processes
A linear stochastic biharmonic heat equation: hitting probabilities
info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion