Multipoint initial-final problem for one class of Sobolev type models of higher order with additive "white noise"

Sobolev type equations theory has been an object of interest in recent years, with much attention being devoted to deterministic equations and systems. Still, there are also mathematical models containing random perturbation, such as white noise. A new concept of "white noise", originally constructed for finite dimensional spaces, is extended here to the case of infinite dimensional spaces. The main purpose is to develop stochastic higher-order Sobolev type equations theory and provide some practical applications. The main idea is to construct "noise" spaces using the Nelson–Gliklikh derivative. Abstract results concerning initial-final problems for higher order Sobolev type equations are applied to the Boussinesq–Love model with additive "white noise". We also use well-known methods in the investigation of Sobolev type equations, such as the phase space method, which reduces a singular equation to a regular one, as defined on some subspace of the initial space.