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Central limit theorem with rate of convergence under sublinear expectations

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  • Zhou, Qianqian
  • Sakhanenko, Alexander
  • Guo, Junyi

Abstract

We study rates of convergence in a central limit theorem (CLT) under sublinear expectations. We consider the form of the CLT introduced by Fang, Peng, Shao, and Song in their work in Bernoulli, 2019, where they investigated the case of Lipschitz functions. Under more general assumptions we obtain estimates in the CLT for arbitrary functions in terms of truncated third moments. Instead of using viscosity solutions of a nonlinear parabolic PDE, which is the main tool in investigations of the CLT under sublinear expectations, here we employ a simpler generalized Lindeberg method.

Suggested Citation

  • Zhou, Qianqian & Sakhanenko, Alexander & Guo, Junyi, 2024. "Central limit theorem with rate of convergence under sublinear expectations," Stochastic Processes and their Applications, Elsevier, vol. 172(C).
    • Handle: RePEc:eee:spapps:v:172:y:2024:i:c:s0304414924000590
    DOI: 10.1016/j.spa.2024.104353
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    References listed on IDEAS

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    1. Freddy Delbaen & Shige Peng & Emanuela Rosazza Gianin, 2010. "Representation of the penalty term of dynamic concave utilities," Finance and Stochastics, Springer, vol. 14(3), pages 449-472, September.
    2. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
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