Limit theorems with rate of convergence under sublinear expectations

DOI10.3150/18-BEJ1063zbMath1428.62096arXiv1711.10649OpenAlexW2972580858MaRDI QIDQ2325334

Shige Peng, Xiao Fang, Yongsheng Song, Qui-Man Shao

Publication date: 25 September 2019

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.10649

zbMATH Keywords

rate of convergenceStein's methodlaw of large numberscentral limit theoremsublinear expectation\(G\)-normal distribution

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Strong limit theorems (60F15)

Related Items (14)

Distributional Uncertainty of the Financial Time Series Measured by $G$-Expectation ⋮ Laws of large numbers under model uncertainty with an application to \(m\)-dependent random variables ⋮ A central limit theorem for sets of probability measures ⋮ Stein's method for the law of large numbers under sublinear expectations ⋮ Convergence rate of Peng's law of large numbers under sublinear expectations ⋮ Discrete‐time approximation for stochastic optimal control problems under the G‐expectation framework ⋮ A central limit theorem, loss aversion and multi-armed bandits ⋮ The sufficient and necessary conditions of the strong law of large numbers under sub-linear expectations ⋮ A universal robust limit theorem for nonlinear Lévy processes under sublinear expectation ⋮ Prokhorov Distance with Rates of Convergence under Sublinear Expectations ⋮ Probabilistic approach to singular perturbations of viscosity solutions to nonlinear parabolic PDEs ⋮ Equivalent conditions of complete \(p\)th moment convergence for weighted sums of i. i. d. random variables under sublinear expectations ⋮ A hypothesis-testing perspective on the \(G\)-normal distribution theory ⋮ Stein's method of normal approximation: some recollections and reflections

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