Abstract

Peng Shige introduced the notions of g-expectation and conditional g-expectation, which is the nonlinear extension of classic
mathematical expectation and conditional mathematical expectation. Just as g-expectation preserves most properties
of classic mathematical expectation except the linearity, conditional g-expectation preserves most properties of classic
conditional mathematical expectation except the linearity. Based on the properties and theorems of classic conditional
mathematical expectation, this paper will discuss and sum up some properties and convergence theorems of conditional
g-expectation.

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