Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths

Denis L.; Hu M.; Peng S.

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Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths

机译：次线性期望相关的函数空间和容量：在G-布朗运动路径中的应用

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In this paper we give some basic and important properties of several typical Banach spaces of functions of G-Brownian motion paths induced by a sublinear expectation-G-expectation. Many results can be also applied to more general situations. A generalized version of Kolmogorov's criterion for continuous modification of a stochastic process is also obtained. The results can be applied in continuous time dynamic and coherent risk measures in finance, in particular for path-dependence risky positions under situations of volatility model uncertainty.

机译：在本文中，我们给出了由亚线性期望-G-期望引起的G-布朗运动路径的几个典型Banach函数空间的一些基本和重要性质。许多结果也可以应用于更一般的情况。还获得了用于连续修改随机过程的Kolmogorov准则的广义形式。该结果可用于金融中连续的时间动态和连贯的风险度量，特别是在波动率模型不确定性情况下的路径依赖风险头寸。

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《Potential analysis: An international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis》 |2011年第2期|共23页
作者
Denis L.; Hu M.; Peng S.;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Capacity; Dynamic programming principle; G-Brownian motion; G-expectation; Sublinear expectation;

机译：容量;动态规划原理;G-布朗运动;G-期望;亚线性期望;

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1. Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths [J] . Laurent Denis, Mingshang Hu, Shige Peng Potential Analysis . 2011,第2期

机译：与亚线性期望相关的函数空间和容量：在G-布朗运动路径中的应用
2. Constructing sublinear expectations on path space [J] . Nutz M., Van Handel R. Stochastic Processes and Their Applications: An Official Journal of the Bernoulli Society for Mathematical Statistics and Probability . 2013,第8期

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3. Variable Exponent Function Spaces related to a Sublinear Expectation [J] . Bochi Xu Abstract and applied analysis . 2020,第16期

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7. Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths [O] . Laurent Denis, Mingshang Hu, Shige Peng 2010

机译：与Sublinear期望相关的功能空间和容量：在G-Brownian运动路径中的应用

Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths

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