A New Central Limit Theorem under Sublinear Expectations

Abstract

We describe a new framework of a sublinear expectation space and the related notions and results of distributions, independence. A new notion of G-distributions is introduced which generalizes our G-normal-distribution in the sense that mean-uncertainty can be also described. W present our new result of central limit theorem under sublinear expectation. This theorem can be also regarded as a generalization of the law of large number in the case of mean-uncertainty.

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• On the laws of the iterated logarithm under the sub-linear expectations without the assumption on the continuity of capacities
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• General laws of large numbers under sublinear expectations
• G-Gaussian Processes under Sublinear Expectations and q-Brownian Motion in Quantum Mechanics
• G-Expectation Weighted Sobolev Spaces, Backward SDE and Path Dependent PDE
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• Gradient Estimates for Nonlinear Diffusion Semigroups by Coupling Methods
• The Independence under Sublinear Expectations
• On representation theorem of sublinear expectation related to G-Lévy process and paths of G-Lévy process
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• A note on pricing of contingent claims under G-expectation
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• Spatial and Temporal white noises under sublinear G-expectation
• A hypothesis-testing perspective on the G-normal distribution theory