Central limit theorem under uncertain linear transformations

We prove a variant of the central limit theorem for a sequence of i.i.d. random variables ξjξj, perturbed by a stochastic sequence of linear transformations AjAj, representing the model uncertainty. The limit, corresponding to a “worst” sequence AjAj, is expressed in terms of the viscosity solution of the GG-heat equation. Our proof is based on the technique of half-relaxed limits.