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Acta Mathematicae Applicatae Sinica 2014年第3期30卷 589-610页

作者： Xue-peng BAI Yi-qing LIN Institut de Recherche Mathématique de Rennes Université de Rennes1 School of Mathematics Shandong University Institut de Recherche Mathématique de Rennes Université de Rennes

In this paper, we study the existence and uniqueness of solutions to stochastic differential equations driven by g-brownian motion （gSDEs） with integral-Lipschitz coefficients.

关键词： g-brownian motion g-expectation g-stochastic differential equations g-backward stochastic differential equations integral-Lipschitz condition

Reflected stochastic differential equations driven by g-brownian motion with nonlinear resistance

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Frontiers of Mathematics in China 2016年第1期11卷 123-140页

作者： Peng LUO School of Mathematics and Qilu Securities Institute for Financial Studies Shandong University Jinan 250100 China Department of Mathematics and Statistics University of Konstanz Konstanz 78457 Germany

We study the uniqueness and existence of solutions of reflected g-stochastic differential equations （RgSDEs） with nonlinear resistance under an integral-Lipschitz condition of coefficients. Moreover, we obtain the c... 详细信息

关键词： g-brownian motion g-expectation reflected g-stochasticdifferential equation (RgSDE) nonlinear resistance comparison theorem

On Representation Theorem of g-Expectations and Paths of g-brownian motion

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Acta Mathematicae Applicatae Sinica 2009年第3期25卷 539-546页

作者： Ming-shang Hu Shi-ge Peng Institute of Mathematics Shandong University Jinan 250100 China

We give a very simple and elementary proof of the existence of a weakly compact family of probability measures {Pθ ： θ∈θ} representing an important sublinear expectation- g-expectation E[·]. We also give a concrete approximation of a bounded continuous function X（ω） by an increasing sequence of cylinder functions Lip（Ω） in order to prove that Cb（Ω） belongs to the completion of Lip（Ω） under the natural norm E[｜·｜].

关键词： Probability and distribution uncertainty g-normal distribution g-brownian motion continuous paths

Some Properties of Stochastic Differential Equations Driven by the g-brownian motion

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Acta Mathematica Sinica,English Series 2013年第5期29卷 923-942页

作者： Qian LIN Institute for Financial Studies Shandong University

In this paper, we study the property of continuous dependence on the parameters of stochastic integrals and solutions of stochastic differential equations driven by the g-brownian motion. In addition, the uniqueness a... 详细信息

关键词： g-expectation continuous paths g-brownian motion stochastic differential equations

The Support of the Solution for Stochastic Differential Equations Driven by g-brownian motion

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Acta Mathematica Sinica,English Series 2012年第12期28卷 2417-2430页

作者： Fu Qing gAO Ming Zhou XU Department of Mathematics and Statistics Wuhan University

By a linear interpolation approximation method, we obtain a characterization of the support of the solution for stochastic differential equations driven by g-brownian motion.

关键词： g-brownian motion g-stochastic differential equation support theorem

Numerical simulations for g-brownian motion

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Frontiers of Mathematics in China 2016年第6期11卷 1625-1643页

作者： Jie YANg Weidong ZHA0 School of Mathematics & Finance Institute Shandong University Jinan 250100 China

This paper is concerned with numerical simulations for the g- brownian motion （defined by S. Peng in Stochastic Analysis and Applications, 2007, 541-567）. By the definition of the g-normal distribution, we first show that the g-brownian motions can be simulated by solving a certain kind of Hamilton-Jacobi-Bellman （HJB） equations. Then, some finite difference methods are designed for the corresponding HJB equations. Numerical simulation results of the g-normal distribution, the g-brownian motion, and the corresponding quadratic variation process are provided, which characterize basic properties of the g-brownian motion. We believe that the algorithms in this work serve as a fundamental tool for future studies, e.g., for solving stochastic differential equations （SDEs）/stochastic partial differential equations （SPDEs） driven by the g-brownian motions.

关键词： Nonlinear expectation g-brownian motion g-normal distribu- tion Hamilton-Jacobi-Bellman (HJB) equation

Harnack Inequality and Applications for SDEs Driven by g-brownian motion

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Acta Mathematicae Applicatae Sinica 2020年第3期36卷 627-635页

作者： Fen-fen YANg Center for Applied Mathematics Tianjin UniversityTianjin 300072China

In this paper,Wang's Harnack and shift Harnack inequality for a class of stochastic differential equations driven by g-brownian motion are *** results generalize the ones in the linear expectation ***,some application... 详细信息

关键词： Harnack inequality shift Harnack inequality stochastic differential equations g-brownian motion g-expectation

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： sublinear expectation capacity g-normal distribution g-brownian motion increments of gbrownian motion law of iterated logarithm

Differentiability of stochastic differential equations driven by the g-brownian motion

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Science China Mathematics 2013年第5期56卷 1087-1107页

作者： LIN Qian Institute of Mathematical Economics Bielefeld University

In this paper,we study the differentiability of the solutions of stochastic differential equations driven by the g-brownian motion with respect to the initial data and the parameter.

关键词： g-expectation g-brownian motion differentiability stochastic differential equations

Optimal control with delayed information flow of systems driven by g-brownian motion

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Probability, Uncertainty and Quantitative Risk 2018年第1期3卷 229-252页

作者： Francesca Biagini Thilo Meyer-Brandis BerntØksendal Krzysztof Paczka Department of Mathematics LMU MunichTheresienstraße 3980333 MunichGermany Department of Mathematics University of OsloP.O.Box 1053 BlindernN-0316 OsloNorway Department of Mathematics University of MunichTheresienstraße 3980333 MunichGermany

In this paper,we study strongly robust optimal control problems under volatility *** the g-framework,we adapt the stochastic maximum principle to find necessary and sufficient conditions for the existence of a strongl... 详细信息

关键词： g-brownian motion optimal control problem stochastic maximum principle