Function spaces and capacity related to a Sublinear Expectation: application to G-Brownian Motion Pathes

Laurent Denis; Mingshang Hu; Shige Peng

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arXiv · 0802.1240

Function spaces and capacity related to a Sublinear Expectation: application to G-Brownian Motion Pathes

Laurent Denis·Mingshang Hu·Shige Peng

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Abstract

In this paper we give some basic and important properties of several typical Banach spaces of functions of $G$-Brownian motion pathes 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 to continuous time dynamic and coherent risk measures in finance in particular for path-dependence risky positions under situations of volatility model uncertainty.

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Laurent Denis, Mingshang Hu, Shige Peng. 2010-01-15. Function spaces and capacity related to a Sublinear Expectation: application to G-Brownian Motion Pathes. https://arxiv.org/abs/0802.1240

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