Central limit theorem under uncertain linear transformations [article]

Dmitry B. Rokhlin
2015 arXiv   pre-print
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 of
more » ... half-relaxed limits from the theory of approximation schemes for fully nonlinear partial differential equations.
arXiv:1505.01084v2 fatcat:epq3gzwvp5b4jnwcq45qyevyhe