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We prove a variant of the central limit theorem (CLT) for a sequence of i.i.d. random variables ξ_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 ofarXiv:1505.01084v2 fatcat:epq3gzwvp5b4jnwcq45qyevyhe