Potential Analysis

, Volume 34, Issue 2, pp 139–161 | Cite as

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

  • Laurent Denis
  • Mingshang Hu
  • Shige Peng


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.


Capacity Sublinear expectation G-expectation G-Brownian motion Dynamic programming principle 

Mathematics Subject Classifications (2010)

60G05 60G17 31A15 


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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Département de Mathématiques, Equipe “Analyse et Probabilités”Université d’Evry-Val-d’EssonneEVRY CedexFrance
  2. 2.School of MathematicsShandong UniversityJinanChina
  3. 3.School of MathematicsFudan UniversityShanghaiChina

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