Central limit theorem under uncertain linear transformations

Dmitry B. Rokhlin

Statistics & Probability Letters, 2015, vol. 107, issue C, 191-198

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

Keywords: Central limit theorem; Model uncertainty; G-heat equation; Viscosity solution; Half-relaxed limits (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spl.2015.08.027

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