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Central limit theorem under uncertain linear transformations

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  • Rokhlin, Dmitry B.

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.

Suggested Citation

  • Rokhlin, Dmitry B., 2015. "Central limit theorem under uncertain linear transformations," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 191-198.
    • Handle: RePEc:eee:stapro:v:107:y:2015:i:c:p:191-198
    DOI: 10.1016/j.spl.2015.08.027
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    References listed on IDEAS

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    1. Peng, Shige, 2008. "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2223-2253, December.
    2. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
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