Sentence examples for linear expectation from inspiring English sources

The well-known Allais [39] and Ellsberg [40] paradox indicates that the classical von-Neumann-Morgenstern linear expected utility theory (here we mean that the linear expectation (mathbb{E}) is used) cannot exactly express people's subjective preferences or criterion involving risk.

Let E be a linear expectation.

Many powerful inequations and conventional methods for linear expectation and probabilities are no longer valid, the study of limit theorems under sub-linear expectation becomes much more challenging.

(mathcal{E}_{0} ) is a minimal member of S; (mathcal{E}_{0} ) is a linear expectation.

(mathcal{E} ) is a minimal member of (S^{mathrm{sl}}); (mathcal{E} ) is a linear expectation.

(mathcal{E}_{0} ) is a maximal member of S; (mathcal{E}_{0} ) is a linear expectation.

He also established the general theoretical framework of the sub-linear expectation space.

The central limit theorem under the sub-linear expectation was first established by Peng (2008b).

The triple Open image in new window is called a sub-linear expectation space.

Peng (2006, 2008a,b) introduced a general framework of the sub-linear expectation of random variables and the notions of the G-normal random variable, G-Brownian motion, independent and identically distributed random variables, etc., under the sub-linear expectation.

In Section 3, the complete convergence and complete moment convergence under sub-linear expectation space are established.