  We prove a variant of the central limit theorem (CLT) for a sequence of
i.i.d. random variables $\xi_j$, perturbed by a stochastic sequence of linear
transformations $A_j$, representing the model uncertainty. The limit,
corresponding to a "worst" sequence $A_j$, is expressed in terms of the
viscosity solution of the $G$-heat equation. In the context of the CLT under
sublinear expectations this nonlinear parabolic equation appeared previously in
the papers of S.Peng. Our proof is based on the technique of half-relaxed
limits from the theory of approximation schemes for fully nonlinear partial
differential equations.
