Law of large numbers and central limit theorem under nonlinear expectations

From MaRDI portal
Publication:2296125

DOI10.1186/s41546-019-0038-2zbMath1434.60075arXivmath/0702358OpenAlexW1619630513MaRDI QIDQ2296125

Shige Peng

Publication date: 17 February 2020

Published in: Probability, Uncertainty and Quantitative Risk (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702358




Related Items

Laws of large numbers under model uncertainty with an application to \(m\)-dependent random variablesMaximally Distributed Random Fields under Sublinear ExpectationStrong law of large numbers under moment restrictions in sublinear expectation spacesHeyde's theorem under the sub-linear expectationsA central limit theorem for sets of probability measuresStein's method for the law of large numbers under sublinear expectationsExtended conditional \(G\)-expectations and related stopping timesOn the laws of the iterated logarithm with mean-uncertainty under sublinear expectationsLimit theorems for delayed sums under sublinear expectationG-Gaussian processes under sublinear expectations and \(q \)-Brownian motion in quantum mechanicsOn the Hartman–Wintner law of the iterated logarithm under sublinear expectationCentral limit theorem for linear processes generated by m-dependent random variables under the sub-linear expectationNew proofs of Khinchin's law of large numbers and Lindeberg's central limit theorem-PDE's approachThe laws of large numbers for Pareto-type random variables under sub-linear expectationDifferentiability of stochastic differential equations driven by the \(G\)-Brownian motionUnnamed ItemWeak and strong limit theorems for stochastic processes under nonadditive probabilityCentral limit theorem for linear processes generated by IID random variables under the sub-linear expectationA new proof of central limit theorem for i.i.d. random variablesA hypothesis-testing perspective on the \(G\)-normal distribution theoryExplicit positive solutions to \(G\)-heat equations and the application to \(G\)-capacitiesThe PDEs and numerical scheme for derivatives under uncertainty volatilityRetracted: Sublinear expectation nonlinear regression for the financial risk measurement and managementOn complete convergence for extended independent random variables under sub-linear expectationsA strong law of large numbers for weighted sums of i.i.d. random variables under capacitiesNotes on Peng's independence in sublinear expectation theory



Cites Work