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Chaos expansion solutions of a class of magnetic Schrödinger Wick-type stochastic equations on $\mathbb{R}^d$
Published 30 Dec 2023 in math.AP and math.PR | (2401.00325v2)
Abstract: We treat some classes of linear and semilinear stochastic partial differential equations of Schr\"odinger type on $\mathbb{R}d$, involving a non-flat Laplacian, within the framework of white noise analysis, combined with Wiener-It^o chaos expansions and pseudodifferential operator methods. The initial data and potential term of the Schr\"odinger operator are assumed to be generalized stochastic processes that have spatial dependence. We prove that the equations under consideration have unique solutions in the appropriate (intersections of weighted) Sobolev-Kato-Kondratiev spaces.
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