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>>
相关基金：国家自然科学基金国家重点基础研究发展计划国家教育部博士点基金中国博士后科学基金更多>>
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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 
O(1/t) complexity analysis of the generalized alternating direction method of multipliers被引量：1
《Science China Mathematics》2019年第4期795-808,共14页Xingju Cai Deren Han 
supported by a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions;National Natural Science Foundation of China (Grant Nos. 11401315, 11625105, 11171159 and 11431102);the National Science Foundation from Jiangsu Province (Grant No. BK20140914)
Owing to its efficiency in solving some types of large-scale separable optimization problems with linear constraints, the convergence rate of the alternating direction method of multipliers(ADMM for short) has recentl...
关键词：generalized ALTERNATING direction method of MULTIPLIERS SEPARABLE CONVEX optimization ITERATION complexity SUBLINEAR convergence rate 
Existence of solutions for sub-linear or super-linear operator equations
《Science China Mathematics》2015年第8期1653-1664,共12页CHEN YingYing DONG YuJun SHAN Yuan 
supported by National Natural Science Foundation of China(Grant No.11171157);the Jiangsu Planned Projects for Postdoctoral Research Funds
We investigate solutions to superlinear or sublinear operator equations and obtain some abstract existence results by minimax methods. These results apply to superlinear or sublinear Hamiltonian systems satisfying sev...
关键词：SUPERLINEAR SUBLINEAR operator equations existence of solutions minimax methods Hamiltoniansystems 
How big are the increments of G-Brownian motion?被引量：4
《Science China Mathematics》2014年第8期1687-1700,共14页HU Feng CHEN ZengJing ZHANG DeFei 
supported by National Natural Science Foundation of China (Grant Nos. 11301295 and 11171179);supported by National Natural Science Foundation of China (Grant Nos. 11231005 and 11171062);supported by National Natural Science Foundation of China (Grant No. 11301160);Natural Science Foundation of Yunnan Province of China (Grant No. 2013FZ116);Doctoral Program Foundation of Ministry of Education of China (Grant Nos. 20123705120005 and 20133705110002);Postdoctoral Science Foundation of China (Grant No. 2012M521301);Natural Science Foundation of Shandong Province of China (Grant Nos. ZR2012AQ009 and ZR2013AQ021);Program for Scientific Research Innovation Team in Colleges and Universities of Shandong Province;WCU (World Class University) Program of Korea Science and Engineering Foundation (Grant No. R31-20007)
In this paper,we investigate the problem:How big are the increments of G-Brownian motion.We obtain the Csrg and R′ev′esz’s type theorem for the increments of G-Brownian motion.As applications of this result,we get ...
关键词：sublinear expectation capacity G-normal distribution G-Brownian motion increments of GBrownian motion law of iterated logarithm 
Large deviation principle for diffusion processes under a sublinear expectation被引量：2
《Science China Mathematics》2012年第11期2205-2216,共12页CHEN ZengJing 1,2 & XIONG Jie 3,4,1 School of Mathematics,Shandong University,Jinan 250100,China 2 Department of Financial Engineering,Ajou University,Suwon 443749,Korea 3 Department of Mathematics,University of Macao,PO Box 3001,Macao,China 4 Department of Mathematics,University of Tennessee,Knoxville,TN 37996-1300,USA 
supported by National Natural Science Foundation of China (Grant No.10921101);WCU program of the Korea Science and Engineering Foundation (Grant No. R31-20007);National Science Foundation of US (Grant No. DMS-0906907)
We represent the exponential moment of the Brownian functionals under a nonlinear expectation according to the solution to a backward stochastic differential equation.As an application,we establish a large deviation p...
关键词：large deviation principle backward stochastic differential equation G-EXPECTATION AMBIGUITY 
Moment bounds for IID sequences under sublinear expectations被引量：6
《Science China Mathematics》2011年第10期2155-2160,共6页HU Feng1,2 1Department of Mathematics,Qufu Normal University,Qufu 273165,China 2School of Mathematics,Shandong University,Jinan 250100,China 
supported in part by National Basic Research Program of China (973 Program) (Grant No. 2007CB814901);the Natural Science Foundation of Shandong Province (Grant No. ZR2009AL015)
With the notion of independent identically distributed(IID) random variables under sublinear expectations introduced by Peng,we investigate moment bounds for IID sequences under sublinear expectations. We obtain a mom...
关键词：moment bound sublinear expectation IID random variables G-normal distribution central limit theorem 
A general central limit theorem under sublinear expectations被引量：16
《Science China Mathematics》2010年第8期1989-1994,共6页LI Min & SHI YuFeng School of Mathematics,Shandong University,Jinan 250100,China 
supported by National Natural Science Foundation of China (Grant No.10771122);Natural Science Foundation of Shandong Province of China (Grant No.Y2006A08);National Basic Research Program of China (Grant No.2007CB814900)
Under some weaker conditions,we give a central limit theorem under sublinear expectations,which extends Peng's central limit theorem.
关键词：central LIMIT THEOREM SUBLINEAR EXPECTATION G-normal distribution 
Survey on normal distributions,central limit theorem,Brownian motion and the related stochastic calculus under sublinear expectations被引量：54
《Science China Mathematics》2009年第7期1391-1411,共21页PENG ShiGe Institute of Mathematics,Shandong University,Jinan 250100,China 
supported by National Basic Research Program of China (Grant No.2007CB814900)(Financial Risk)
This is a survey on normal distributions and the related central limit theorem under sublinear expectation.We also present Brownian motion under sublinear expectations and the related stochastic calculus of It's type....
关键词：probability and distribution uncertainty normal distribution Brownian motion central limit theorem 60H10 60H05 60H30 60E05 60E07 62C05 62D05 
The minimal sublinear expectations and their related properties被引量：5
《Science China Mathematics》2009年第4期785-793,共9页JIA GuangYan School of Mathematics, Shandong University, Jinan 250100, China 
supported by National Basic Research Program of China (973 Program) (Grant No.2007CB814901) (Financial Risk);National Natural Science Foundation of China (Grant No. 10671111)
In this paper, we prove that for a sublinear expectation ?[·] defined on L 2(Ω, $ \mathcal{F} $ ), the following statements are equivalent: ? is a minimal member of the set of all sublinear expectations defined on L...
关键词：G-EXPECTATION Jensen’s inequality linear expectation subadditive expectation sublinear expectation 60H10 
Boundedness of solutions for sublinear reversible systems
《Science China Mathematics》2001年第2期137-144,共8页黎雄 
The author is very grateful to Professors Ding Tongren and Liu Bin for their valuable suggestions for this paper.
We are concerned with the boundedness of all the solutions for second order differential equation $$\ddot x + f\left( x \right)\dot x + g\left( x \right) = e\left( t \right),$$ , wheref(x) andg(x) are odd, e( t) is od...
关键词：boundedness of solutions invariant tori reversible systems 
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