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Strong laws of large numbers for sub-linear expectations

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Science China Mathematics 2016年第5期59卷 945-954页

作者： chen zengjing School of Mathematics Shandong University

We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed(IID) random variables for sub-linear expectations initiated by *** turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's strong law of large numbers to the case where probability measures are no longer additive. An important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities.

关键词：次线性 Kolmogorov 强大数定律法律独立同分布随机变量频率统计添加剂

Invariance principles for the law of the iterated logarithm under G-framework

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Science China Mathematics 2015年第6期58卷 1251-1264页

作者： WU PanYu chen zengjing Qilu Securities Institute for Financial Studies Shandong University School of Mathematics Shandong University

We obtain a general invariance principle of G-Brownian motion for the law of the iterated logarithm(LIL for short). For continuous bounded independent and identically distributed random variables in G-expectation space, we also give an invariance principle for LIL. In some sense, this result is an extension of the classical Strassen's invariance principle to the case where probability measure is no longer additive. Furthermore,we give some examples as applications.

关键词：不变性原理法律原则对数框架不变原理布朗运动随机变量空间分布

How big are the increments of G-Brownian motion?

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Science China Mathematics 2014年第8期57卷 1687-1700页

作者： HU Feng chen zengjing ZHANG DeFei School of Mathematical Sciences Qufu Normal University School of Mathematics Shandong University Department of Financial Engineering Ajou University Department of Mathematics Honghe University

In this paper,we investigate the problem:How big are the increments of G-Brownian *** obtain the Csrg and R′ev′esz’s type theorem for the increments of G-Brownian *** applications of this result,we get the law of iterated logarithm and the Erds and R′enyi law of large numbers for G-Brownian ***,it turns out that our theorems are natural extensions of the classical results obtained by Csrg and R′ev′esz(1979).

关键词：布朗运动增量 ERD EV 定理铯

Existence and uniqueness for BSDE with stopping time

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Chinese Science Bulletin 1998年第2期43卷 96-99页

作者： chen zengjing Department of Mathematics, Shandong University, Jinan 250100, China Department of Mathematics Shandong University Jinan China

The existence and uniqueness of the solutions for a class of backward stochastic differential equations (BSDEs for short) in a random interval are discussed.

关键词： BSDE stopping time adapted solution.

CONTINUOUS PROPERTIES OF G-MARTINGALES

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Chinese Annals of Mathematics,Series B 2001年第1期22卷 115-128页

作者：陈曾敬彭实戈 DepartmentofMathematics ShandongUniversityJinan250100China

The authors study the continuous properties of square integrable g-martingales via backward stochastic differential equations (shortly BSDEs) and get a general upcrossing inequality and an optional stopping theorem fo... 详细信息

关键词：连续性 G-鞅随意停机定理随机微分方程

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概率统计由线性到非线性的发展

数学建模及其应用 2023年第2期12卷 125-134页

作者：陈增敬冯新伟山东大学数学学院山东济南250100 山东大学中泰证券金融研究院山东济南250100

概率统计是研究不确定现象的数学学科,它的本质就是从不确定现象中找确定的统计规律.三百多年以来,概率统计不仅推动了数学由确定性数学到随机数学的发展,也为经济、金融、物理、化学和生物等学科的发展提供了有效的计量工具和方法.随... 详细信息

概率统计是研究不确定现象的数学学科,它的本质就是从不确定现象中找确定的统计规律.三百多年以来,概率统计不仅推动了数学由确定性数学到随机数学的发展,也为经济、金融、物理、化学和生物等学科的发展提供了有效的计量工具和方法.随着大数据、人工智能和经济金融的飞速发展,现代概率统计已不能满足经济和科技发展的需要,发展和创新概率统计,为大数据、人工智能和经济金融提供理论基础和计算方法已是数学家攻克的重点热点问题.为了满足概率统计爱好者的需要,本文简单地介绍了概率统计发展的过程、对科学发展的作用、面临的问题和目前正在开展的新的研究方向,从另一个侧面介绍一下概率统计前世与后生.

关键词：概率论极限定理金融革命非线性期望非线性正态分布

关于倒向随机微分方程生成元惟一性的一个结果

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应用数学学报 2010年第1期33卷 51-58页

作者：胡锋陈增敬山东大学数学学院济南250100

在本文中,在假定倒向随机微分方程的标准参数满足较弱条件的前提下,我们证明了倒向随机微分方程的生成元由相对应的倒向随机微分方程的终端条件所得到的初始值惟一决定.这个结果从另一方面也论证和推广了Peng的推测.

关键词：倒向随机微分方程(BSDE) 生成元比较定理

Meridional deflection of global eddy propagation derived from tandem altimetry: Mechanism and implication

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Science China Earth Sciences 2024年第3期67卷 811-825页

作者： Ge chen Xiaoyan chen Frontiers Science Center for Deep Ocean Multispheres and Earth System School of Marine TechnologyOcean University of ChinaQindao 266100China Laboratory for Regional Oceanography and Numerical Modeling Laoshan LaboratoryQindao 266237China

A common view on meridional deflection of eddy propagation is poleward for cyclones and equatorward for anticyclones. This widely accepted polarity-sensitive pattern has been increasingly undermined given that it is systematically violated on both zonal and regional scales as recently reported. Here, we approach the problem by exploring these violations in terms of eddy effects of spatiotemporal geostrophy, thermal fading, and flow dragging, yielding the following main conclusions.(1) The polarity-dependent deflection discrepancy is a pseudo feature resulting from a biased fit to the normalized eddy tracks which are spatially asymmetric(though azimuthally symmetric) between the two signs;Instead, the primary pattern of eddy deflection appears to be geographically correlated and polarity independent.(2) Geostrophic adjustment plays a critical role in defining the meridional movement of an eddy. Specifically, a consistent poleward(equatorward) trajectory bending of spatially(temporally) ageostrophic eddies is observed irrespective of their polarity.(3) The mechanism of eddy deflection is also determined by its zonal propagation direction. Westward propagating eddies are substantially affected by thermal fading, while opposite ones by flow dragging. A realistic and comprehensive understanding of eddy deflection mechanisms serves as a significant contribution to the prediction of eddy trajectory, and the protection of ocean environment.

关键词： Mesoscale eddies Eddy propagation Eddy meridional deflection Satellite observation Geostrophic adjustment

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气象业务综合平台设计与实现

长江信息通信 2022年第1期35卷 107-109页

作者：吴晓岳勇陈增境中国气象局旱区特色农业气象木灾害监测预警与风险管理重点实验室宁夏银川750002 石嘴山市气象局宁夏石嘴山753000 宁夏气象信息中心宁夏银川750002

为满足气象监测、预报、服务等多方面气象业务需求,需建设全面支撑的一体化气象业务平台。石嘴山市气象业务综合平台构建了立体气象监测网,融合多种监测资料,结合GIS技术实时展示和处理气象信息,实现了气象实时监测到服务产品一体化生成... 详细信息

为满足气象监测、预报、服务等多方面气象业务需求,需建设全面支撑的一体化气象业务平台。石嘴山市气象业务综合平台构建了立体气象监测网,融合多种监测资料,结合GIS技术实时展示和处理气象信息,实现了气象实时监测到服务产品一体化生成,简化了气象服务流程,提高了气象预警时效,有效提升了石嘴山市气象服务的工作效率和服务效果。

关键词：地理信息业务一体化数据可视化气象服务气象预警