极限理论在概率论的研究中具有举足轻重的地位.在Kolmogorov公理体系下,从最初的Bernoulli大数定律到一般形式的中心极限定理,随机变量的独立同分布(independent and identically distributed,IID)假设伴随了概率论的兴起与发展.此时,...极限理论在概率论的研究中具有举足轻重的地位.在Kolmogorov公理体系下,从最初的Bernoulli大数定律到一般形式的中心极限定理,随机变量的独立同分布(independent and identically distributed,IID)假设伴随了概率论的兴起与发展.此时,中心极限定理与此相应的正态分布在概率论中占据着“中心”地位.然而,当随机变量不满足IID的条件时,数学家们已经发现:在非IID情形下,随机变量和的渐近分布很可能不再是正态分布.因此,探讨非IID情形下的极限分布是自正态分布产生200多年以来的一个公开问题,也吸引了很多学者的关注.此外,从经济市场发展的观点看,在Kolmogorov公理体系下,概率论可以很好地量化市场内在的运行规律;但是,Kolmogorov公理体系很难精确地刻画人类行为对经济市场的外在影响,例如,经济界三大著名的悖论表明,在Kolmogorov公理体系下的概率理论在实际应用中具有明显的局限性,有很多不确定现象无法准确地使用线性概率和线性期望建模,这推动了概率由线性向非线性的发展.随着非线性概率研究的兴起,在非线性期望及非IID意义下建立随机变量和的渐近分布的泛化性结论成为一种可能.本文主要介绍经典框架下极限理论的发展史以及非线性期望框架下非线性大数定律、中心极限定理和重对数律的主要结果.展开更多
In this paper, we investigate Markovian backward stochastic differential equations(BSDEs) with the generator and the terminal value that depend on the solutions of stochastic differential equations with rankbased drif...In this paper, we investigate Markovian backward stochastic differential equations(BSDEs) with the generator and the terminal value that depend on the solutions of stochastic differential equations with rankbased drift coefficients. We study regularity properties of the solutions of this kind of BSDEs and establish their connection with semi-linear backward parabolic partial differential equations in simplex with Neumann boundary condition. As an application, we study the European option pricing problem with capital size based stock prices.展开更多
Almost automorphic is a particular case of the recurrent motion, which has been studied in differential equations for a long time. We introduce square-mean pseudo almost automorphic and some of its properties, and the...Almost automorphic is a particular case of the recurrent motion, which has been studied in differential equations for a long time. We introduce square-mean pseudo almost automorphic and some of its properties, and then study the pseudo almost automorphic solution in the distribution sense to stochastic differential equation driven by Levy process.展开更多
To the Editor:The unprecedented pandemic of coronavirus disease 2019(COVID-19)has put tremendous pressure on healthcare resources and economic development worldwide.Severe acute respiratory syndrome coronavirus 2(SARS...To the Editor:The unprecedented pandemic of coronavirus disease 2019(COVID-19)has put tremendous pressure on healthcare resources and economic development worldwide.Severe acute respiratory syndrome coronavirus 2(SARS-CoV-2)Omicron strain has become the dominant causative strain of COVID-19 in most countries since the end of 2021.Although a large cohort study comparing the symptomatic presentation of SARSCoV-2 Omicron and Delta infection has been made in the UK,[1]features and evolution of symptoms of individuals infected with Omicron are rarely reported in other countries or regions,especially among Asian individuals.展开更多
文摘极限理论在概率论的研究中具有举足轻重的地位.在Kolmogorov公理体系下,从最初的Bernoulli大数定律到一般形式的中心极限定理,随机变量的独立同分布(independent and identically distributed,IID)假设伴随了概率论的兴起与发展.此时,中心极限定理与此相应的正态分布在概率论中占据着“中心”地位.然而,当随机变量不满足IID的条件时,数学家们已经发现:在非IID情形下,随机变量和的渐近分布很可能不再是正态分布.因此,探讨非IID情形下的极限分布是自正态分布产生200多年以来的一个公开问题,也吸引了很多学者的关注.此外,从经济市场发展的观点看,在Kolmogorov公理体系下,概率论可以很好地量化市场内在的运行规律;但是,Kolmogorov公理体系很难精确地刻画人类行为对经济市场的外在影响,例如,经济界三大著名的悖论表明,在Kolmogorov公理体系下的概率理论在实际应用中具有明显的局限性,有很多不确定现象无法准确地使用线性概率和线性期望建模,这推动了概率由线性向非线性的发展.随着非线性概率研究的兴起,在非线性期望及非IID意义下建立随机变量和的渐近分布的泛化性结论成为一种可能.本文主要介绍经典框架下极限理论的发展史以及非线性期望框架下非线性大数定律、中心极限定理和重对数律的主要结果.
基金supported by National Science Foundation of USA(Grant No.DMS-1206276)National Natural Science Foundation of China(Grant No.11601280)
文摘In this paper, we investigate Markovian backward stochastic differential equations(BSDEs) with the generator and the terminal value that depend on the solutions of stochastic differential equations with rankbased drift coefficients. We study regularity properties of the solutions of this kind of BSDEs and establish their connection with semi-linear backward parabolic partial differential equations in simplex with Neumann boundary condition. As an application, we study the European option pricing problem with capital size based stock prices.
基金The authors are grateful to the anonymous referees for very helpful comments on the original version of this paper. The work of Xinwei FENG was partially supported by the National Natural Science Foundation of China （Grant No. 11601280）. The work of Gaofeng ZONG was supported in part by the National Natural Science Foundation of China （Grant Nos. 11501325, 11231005） and the China Postdoctoral Science Foundation （Grant No. 2018T110706）.
文摘Almost automorphic is a particular case of the recurrent motion, which has been studied in differential equations for a long time. We introduce square-mean pseudo almost automorphic and some of its properties, and then study the pseudo almost automorphic solution in the distribution sense to stochastic differential equation driven by Levy process.
文摘To the Editor:The unprecedented pandemic of coronavirus disease 2019(COVID-19)has put tremendous pressure on healthcare resources and economic development worldwide.Severe acute respiratory syndrome coronavirus 2(SARS-CoV-2)Omicron strain has become the dominant causative strain of COVID-19 in most countries since the end of 2021.Although a large cohort study comparing the symptomatic presentation of SARSCoV-2 Omicron and Delta infection has been made in the UK,[1]features and evolution of symptoms of individuals infected with Omicron are rarely reported in other countries or regions,especially among Asian individuals.
