Results 231 to 240 of about 39,415 (259)

Strong Convergence Theorems Under Sub-linear Expectations and Its Applications in Nonparametric Regression Models

Communications in Mathematics and Statistics, 2023
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Xuejun Wang, Mengmei Xi
exaly   +2 more sources

Complete Moment Convergence and $$L_q$$ Convergence for AANA Random Variables Under Sub-linear Expectations

Bulletin of the Malaysian Mathematical Sciences Society, 2023
Given a measurable space \((\Omega, \mathcal{F})\), consider a collection \(\mathcal{P}\) of probability measures on \((\Omega, \mathcal{F})\). Now, define the following upper and lower probabilities \[ \mathbb{P}(A) = \sup_{P \in \mathcal{P}} P(A), \text{ and } \mathsf{P}(A) = \inf_{P \in \mathcal{P}} P(A), \tag{1} \] for all \(A\in \mathcal{F ...
Xuejun Wang, Mengmei Xi
exaly   +2 more sources

Heyde’s theorem under the sub-linear expectations

Statistics & Probability Letters, 2021
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The Law of Logarithm for Arrays of Random Variables under Sub-linear Expectations

Acta Mathematicae Applicatae Sinica, English Series, 2020
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Xu, Jia-pan, Zhang, Li-xin
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Another form of Chover’s law of the iterated logarithm under sub-linear expectations

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2019
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Qunying Wu, Jianfang Lu
openaire   +2 more sources

Strong laws of large numbers for sub-linear expectation without independence

Communications in Statistics - Theory and Methods, 2017
ABSTRACTIn this paper, we investigate some strong laws of large numbers for sub-linear expectation without independence which generalize the classical ones. We give some strong laws of large numbers for sub-linear expectation on some moment conditions with respect to the partial sum and some conditions similar to Petrov’s.
Zengjing Chen, Cheng Hu, Gaofeng Zong
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An elementary proof of Peng’s central limit theorem under sub-linear expectations

International Journal of Financial Engineering, 2020
Motivated by studies in mathematical finance, S. Peng established a central limit theorem (CLT) under sub-linear expectations by using partial differential equations (PDEs). In this paper, we provide a novel proof of Peng’s CLT in the frame of sub-linear expectation.
Zengjing Chen, Ziwu Zhang
openaire   +1 more source

Strong Limit Theorems for Weighted Sums under the Sub-linear Expectations

Acta Mathematicae Applicatae Sinica, English Series
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Feng, Feng-xiang, Wang, Ding-cheng, Wu, Qun-ying, Huang, Haiwu   +3 more
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Weak and strong laws of large numbers for sub-linear expectation

Communications in Statistics - Theory and Methods, 2019
AbstractIn this paper, we derive a new form of weak laws of large numbers for sub-linear expectation and establish the equivalence relation among this new form and the other two forms of weak laws ...
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The laws of large numbers for Pareto-type random variables under sub-linear expectation

Frontiers of Mathematics, 2022
Very exciting basic definitions of probability calculation theory are expanded: the relevant conclusions in the traditional probability space are extended to the sub-linear expectation space. From a new aspect, one of the most beautiful theorems of probability calculation, the weak law of large numbers and strong law of large numbers of the weighted ...
Chen, Binxia, Wu, Qunying
openaire   +2 more sources