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The Statistical Exploration In The $G$-Expectation Framework: The Pseudo Simulation And Estimation Of Variance Uncertainty, Yifan Li

Electronic Thesis and Dissertation Repository

The $G$-expectation framework, motivated by problems with \emph{uncertainty}, is a new generalization of the classical probability framework. Similar to the Choquet expectation, the $G$-expectation can be represented as the supremum of a class of linear expectations. In the past two decades, it has developed into a complete stochastic structure connected with a large family of nonlinear PDEs. Nonetheless, to apply it to real-world problems with uncertainty, it is fundamentally necessary to build up the associated statistical methodology.

This thesis explores the \emph{computation, simulation, and estimation} of the $G$-normal distribution (a typical distribution with variance uncertainty) by constructing a new substructure …