Nonperturbative polaron variational methods are used to study inclusive scattering in the context of the scalar Wick--Cutkosky model. We derive the structure functions for a scalar point-like nucleon surrounded by a cloud of strongly interacting mesons from the Compton amplitude that is obtained in a recent variational calculation based on the particle (or worldline) representation. In zeroth variational order, a covariant exponentiated form is obtained, which is identical to the one suggested by Vineyard for scattering of slow neutrons from quantum liquids. In first order, the much richer dependence of the structure function on momentum and energy transfer, which emerges, is evaluated numerically. We study the Q~2-evolution and the perturbative as well as the scaling limit of our variational structure functions. Finally, the momentum sum rule is derived and evaluated in order to determine the momentum fraction carried by the neutral mesons inside the dressed nucleon.
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