检索结果-南通市图书馆

Spatial and temporal white noises under sublinear G-expectation

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2020年第1期63卷 61-82页

作者： Xiaojun Ji shige peng School of Mathematics Shandong UniversityJinan 250100China Zhongtai Securities Institute for Financial Studies Shandong UniversityJinan 250100China

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 *** on this result,we also introduce a spatial-temporal G-white *** from the case of linear expectation,in which the probability measure needs to be known,under the uncertainty of probability measures,spatial white noises are intrinsically different from temporal cases.

关键词： sublinear expectation G-Brownian motion G-Gaussian random field G-white noise spatial and temporal white noise

Stochastic calculus with respect to G-Brownian motion viewed through rough paths

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2017年第1期60卷 1-20页

作者： peng shige ZHANG HuiLin School of Mathematics Shandong University Jinan 250100 China Institute for Advanced Research Shandong University Jinan 250100 China

We study rough path properties of stochastic integrals of Ito's type and Stratonovich's type with respect to G-Brownian motion. The roughness of G-Brownian motion is estimated and then the pathwise Norris lemma in G-f... 详细信息

关键词： rough paths roughness of G-Brownian motion Norris lemma

BSDE,path-dependent PDE and nonlinear Feynman-Kac formula

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2016年第1期59卷 19-36页

作者： peng shige WANG FaLei School of Mathematics Shandong UniversityJinan 250100China Qilu Institute of Finance Shandong UniversityJinan 250100China Institute for Advanced Research Shandong UniversityJinan 250100China

We introduce a new type of path-dependent quasi-linear parabolic PDEs in which the continuous paths on an interval [0, t] become the basic variables in the place of classical variables （t, x） ∈[0, T]× R^d. This new type of PDEs are formulated through a classical BSDE in which the terminal values and the generators are allowed to be general function of Brownian motion paths. In this way, we establish the nonlinear Feynman- Kac formula for a general non-Markoviau BSDE. Some main properties of solutions of this new PDEs are also obtained.

关键词： backward stochastic differential equation nonlinear Feynman-Kac formula path-dependent PDE

Survey on Path-Dependent PDEs

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of Mathematics,Series B 2023年第6期44卷 837-856页

作者： shige peng Yongsheng SONG Falei WANG School of Mathematics Zhongtai Securities Institute for Financial StudiesShandong UniversityJinan 250100China Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China Zhongtai Securities Institute for Financial Studies School of MathematicsShandong UniversityJinan 250100China

In this paper,the authors provide a brief introduction of the path-dependent partial differential equations(PDEs for short)in the space of continuous paths,where the path derivatives are in the Dupire(rather than Fréchet)*** present the connections between Wiener expectation,backward stochastic differential equations(BSDEs for short)and path-dependent *** also consider the well-posedness of path-dependent PDEs,including classical solutions,Sobolev solutions and viscosity solutions.

关键词： Path-Dependent Wiener expectation BSDEs Classical solution Sobolev solution Viscosity solution

Reflected solutions of backward stochastic differential equations driven by G-Brownian motion

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2018年第1期61卷 1-26页

作者： Hanwu Li shige peng Abdoulaye Soumana Hima School of Mathematics Shandong University Jinan 250100 China Zhongtai Institute of Finance Shangdong University Jinan 250100 China Institut de Recherche Mathdmatiques de Rennes Universitd de Rennes 1 Rennes Cedex 35042 France Departement de Mathdmatiques Universite de Maradi Maradi BP 465 Niger

In this paper, we study the reflected solutions of one-dimensional backward stochastic differential equations driven by G-Brownian motion. The reflection keeps the solution above a given stochastic process. In order to derive the uniqueness of reflected G-BSDEs, we apply a "martingale condition" instead of the Skorohod condition. Similar to the classical case, we prove the existence by approximation via penalization. We then give some applications including a generalized Feynman-Kac formula of an obstacle problem for fully nonlinear partial differential equation and option pricing of American types under volatility uncertainty.

关键词： G-expectation reflected backward stochastic differential equations obstacle problems for fully nonlinear PDEs

Law of large numbers and central limit theorem under nonlinear expectations

在线全文

学校读者我要写书评

暂无评论

Probability, Uncertainty and Quantitative Risk 2019年第1期4卷 72-79页

作者： shige peng Institute of Mathematics Shandong UniversityJinan 250100Shandong ProvinceChina

The main achievement of this paper is the finding and proof of Central Limit Theorem(CLT,see Theorem 12)under the framework of sublinear *** speaking under some reasonable assumption,the random sequence{1/√n(X1+···+Xn)}i∞=1 converges in law to a nonlinear normal distribution,called G-normal distribution,where{Xi}i∞=1 is an *** under the sublinear ***’s known that the framework of sublinear expectation provides a important role in situations that the probability measure itself has non-negligible *** such situation,this new CLT plays a similar role as the one of classical *** classical CLT can be also directly obtained from this new CLT,since a linear expectation is a special case of sublinear expectations.A deep regularity estimate of 2nd order fully nonlinear parabolic PDE is applied to the proof of the *** paper is originally exhibited in arXiv.(***/0702358v1).

关键词： Central limit theorem Nonlinear expectation Probability measure uncertainty

Optimal unbiased estimation for maximal distribution

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Probability, Uncertainty and Quantitative Risk 2021年第3期6卷 189-198页

作者： Hanqing Jin shige peng Mathematical Institute Oxford UniversityOxfordOX12JDUnited Kingdom School of Mathematics Shandong UniversityJinan 250100ShandongChina

Unbiased estimation for parameters of maximal distribution is a fundamental problem in the statistical theory of sublinear *** this paper,we proved that the maximum estimator is the largest unbiased estimator for the ... 详细信息

关键词： Sublinear expectations Maximal distributions Optimal unbiased estimation

Extended conditional G-expectations and related stopping times

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Probability, Uncertainty and Quantitative Risk 2021年第4期6卷 369-390页

作者： Mingshang Hu shige peng Zhongtai Securities Institute for Financial Studies Shandong UniversityJinan 250100ShandongChina School of Mathematics Shandong UniversityJinan 250100ShandongChina

In this paper,we extend the definition of conditional G-expectation to a larger space on which the dynamical consistency still *** can consistently define,by taking the limit,the conditional G-expectation for each random variable X,which is the downward limit(respectively,upward limit)of a monotone sequence (Xi) in L_(G)^(1)(Ω).To accomplish this procedure,some careful analysis is ***,we present a suitable definition of stopping times and obtain the optional stopping *** also provide some basic and interesting properties for the extended conditional G-expectation.

关键词： G-expectation Conditional G-expectation Stopping times Optional stopping theorem

G-Lévy processes under sublinear expectations

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Probability, Uncertainty and Quantitative Risk 2021年第1期6卷 1-22页

作者： Mingshang Hu shige peng Zhongtai Securities Institute for Financial Studies Shandong UniversityJinan 250100ShandongChina School of Mathematics Shandong UniversityJinan 250100ShandongChina

We introduce G-Lévy processes which develop the theory of processes with independent and stationary increments under the framework of sublinear *** then obtain the Lévy-Khintchine formula and the existence for G-Lé... 详细信息

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