SUBLINEAR

作品数：64被引量：170H指数：6
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相关领域：理学更多>>
相关作者：安和平冯恩民游兆永刘辉昭蒋达清更多>>
相关机构：东北师范大学大连理工大学云南工业大学西安交通大学更多>>
相关期刊：《四川师范大学学报（自然科学版）》《Journal of Partial Differential Equations》《Applied Mathematics and Mechanics(English Edition)》《Frontiers of Mathematics in China》更多>>
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On the Necessary and Sufficient Conditions for Peng's Law of Large Numbers Under Sublinear Expectations
《Chinese Annals of Mathematics,Series B》2025年第1期139-150,共12页Xinpeng LI Gaofeng ZONG 
supported by the National Natural Science Foundation of China(Nos.12326603,11601281,11501325);the National Key R&D Program of China(No.2018YFA0703900);the Natural Science Foundation of Shandong Province(No.ZR2021MA018);the Social Science Planning Project of Shandong Province(No.24CJJJ18);the Qilu Scholars Program of Shandong University。
In this paper,the authors firstly establish the weak laws of large numbers on the canonical space(R^(N),B(R^(N)))by traditional truncation method and Chebyshev’s inequality as in the classical probability theory.Then...
关键词：Canonical space Independence and identical distribution Peng's law of large numbers Sublinear expectation 
A strong law of large numbers under sublinear expectations
《Probability, Uncertainty and Quantitative Risk》2023年第3期333-350,共18页Yongsheng Song 
supported by National Key R&D Program of China(Grant Nos.2020YFA0712700,2018YFA0703901);NSFCs(Grant No.11871458);Key Research Program of Frontier Sciences,CAS(Grant No.QYZDBSSW-SYS017).
We consider a sequence of independent and identically distributed(i.i.d.)random variables{ξ_(k)}under a sublinear expectation E=sup_(P∈Θ).We first give a new proof to the fact that,under each P∈Θ,any cluster poin...
关键词：Law of large numbers Tailσ-algebra Sublinear expectation 
Non-linear affine processes with jumps
《Probability, Uncertainty and Quantitative Risk》2023年第2期235-266,共32页Francesca Biagini Georg Bollweg Katharina Oberpriller 
We present a probabilistic construction of R^(d)-valued non-linear affine processes with jumps.Given a setΘof affine parameters,we define a family of sublinear expectations on the Skorokhod space under which the cano...
关键词：Sublinear expectation Non-linear affine processes Dynamic programming PIDE 
A universal robust limit theorem for nonlinear Lévy processes under sublinear expectation
《Probability, Uncertainty and Quantitative Risk》2023年第1期1-32,共32页Mingshang Hu Lianzi Jiang Gechun Liang Shige Peng 
supported by the National Key R&D Program of China(Grant No.2018YFA0703900);the National Natural Science Foundation of China(Grant No.11671231);the Qilu Young Scholars Program of Shandong University;supported by the Tian Yuan Projection of the National Natural Science Foundation of China(Grant Nos.11526205,11626247);the National Basic Research Program of China(973 Program)(Grant No.2007CB814900(Financial Risk)).
This article establishes a universal robust limit theorem under a sublinear expectation framework.Under moment and consistency conditions,we show that,forα∈(1,2),the i.i.d.sequence{(1/√∑_(i=1)^(n)X_(i),1/n∑_(i=1)...
关键词：Universal robust limit theorem Partial integro-differential equation Nonlinear Lévy process α-stable distribution Sublinear expectation 
On the laws of the iterated logarithm with mean-uncertainty under sublinear expectations被引量：1
《Probability, Uncertainty and Quantitative Risk》2022年第1期1-12,共12页Xiaofan Guo Shan Li Xinpeng Li 
supported by NSF of Shandong Province(Grant No.ZR2021MA018);National Key R&D Program of China(Grant No.2018YFA0703900);NSF of China(Grant No.11601281);the Young Scholars Program of Shandong University.
A new Hartman-Wintner-type law of the iterated logarithm for independent random variables with mean-uncertainty under sublinear expectations is established by the martingale analogue of the Kolmogorov law of the itera...
关键词：Law of the iterated logarithm Mean-uncertainty Upper and lower variances Sublinear expectation 
Reduced-form setting under model uncertainty with non-linear affine intensities
《Probability, Uncertainty and Quantitative Risk》2021年第3期159-188,共30页Francesca Biagini Katharina Oberpriller 
In this paper we extend the reduced-form setting under model uncertainty introduced in[5]to include intensities following an affine process under parameter uncertainty,as defined in[15].This framework allows us to int...
关键词：Sublinear expectation Reduced-form framework Non-linear affine processes Arbitrage-free pricing 
Convergence rate of Peng’s law of large numbers under sublinear expectations被引量：2
《Probability, Uncertainty and Quantitative Risk》2021年第3期261-266,共6页Mingshang Hu Xiaojuan Li Xinpeng Li 
This project is supported by National Key R&D Program of China(Grant No.2018YFA0703900);National Natural Science Foundation of China(Grant Nos.11601281,11671231).
This short note provides a new and simple proof of the convergence rate for the Peng’s law of large numbers under sublinear expectations,which improves the results presented by Song[15]and Fang et al.[3].
关键词：Law of large numbers Rate of convergence Sublinear expectation 
G-Lévy processes under sublinear expectations被引量：3
《Probability, Uncertainty and Quantitative Risk》2021年第1期1-22,共22页Mingshang Hu Shige Peng 
This work was supported by National Key R&D Program of China(Grant No.2018YFA0703900);National Natural Science Foundation of China(Grant No.11671231);Tian Yuan Fund of the National Natural Science Foundation of China(Grant Nos.11526205 and 11626247);National Basic Research Program of China(973 Program)(Grant No.2007CB814900).
We introduce G-Lévy processes which develop the theory of processes with independent and stationary increments under the framework of sublinear expectations.We then obtain the Lévy-Khintchine formula and the existen...
关键词：Sublinear expectation G-normal distribution G-Brownian motion G-EXPECTATION Lévy process G-Lévy process G-Poisson process Lévy-Khintchine formula Lévy-Itôdecomposition 
Optimal Contract for the Principal-Agent Under Knightian Uncertainty被引量：3
《Journal of the Operations Research Society of China》2020年第4期637-654,共18页Kun-Lun Wang Chen Fei Wei-Yin Fei 
This research was supported by the National Natural Science Foundation of China(No.71571001).
Under the Knightian uncertainty,this paper constructs the optimal principal(he)-agent(she)contract model based on the principal’s expected profit and the agent’s expected utility function by using the sublinear expe...
关键词：Knightian uncertainty PRINCIPAL-AGENT Sublinear expectation HJB equation Behavioral economics 
Spatial and temporal white noises under sublinear G-expectation
《Science China Mathematics》2020年第1期61-82,共22页Xiaojun Ji Shige Peng 
supported by National Natural Science Foundation of China (Grant No. L1624032)
Under the framework of sublinear expectation,we introduce a new type of G-Gaussian random fields,which contains a type of spatial white noise as a special case.Based on this result,we also introduce a spatial-temporal...
关键词：sublinear expectation G-Brownian motion G-Gaussian random field G-white noise spatial and temporal white noise 
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