Approximation and support theorem for a wave equation in two space dimensions
It is proved a characterization of the topological support of the law induced by a solution for a stochastic wave equation with two-dimensional space variable and driven by a noise, white in time and correlated in space. There are studied: 1. approximation theorems and convergence in probability, 2. equations obtained by smoothing the random noise, 3. approximations in the \(L^p\)-norm, \(p\geq 1\), for some particular classes of coefficients. The paper is recommended to those working in the field of partial differential equations with stochastic perturbations.
stochastic partial differential equations
scientific article; zbMATH DE number 1547287