# name
A linear stochastic biharmonic heat equation: hitting probabilities

# metadata.dc.description.abstract[].value
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.

# metadata.dc.relation.ispartof[].value
Stochastics And Partial Differential Equations-Analysis And Computations, 2022, vol. 10, num. 3, p. 735-756

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
A linear stochastic biharmonic heat equation: hitting probabilities