Linear SPDEs driven by stationary random distributions
A class of linear stochastic partial differential equations (SPDEs) are investigated. The noise might be non-Gaussian but includes spatially homogeneous Gaussian noises and fractional noises. Sufficient conditions imposed on the Green function of the involved differential operator for the existence of a random field solution of a linear SPDE with this type of noise are presented. The main results are applied to the study of the heat and wave equations.
stochastic partial differential equation
scientific article; zbMATH DE number 6132231
scientific article