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

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

2008-02-09

arxiv.org/abs/0802.1240v2

Mathematics

Probability

26 pages

Scientific paper

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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