Sentence examples for linear expectations from inspiring English sources

So Peng [1 5] introduced the notions of sub-linear expectations to extend the classical linear expectations.

Sub-linear expectations generate lots of interesting properties which are unlike those in linear expectations, and the issues in sub-linear expectations are more challenging, so lots of scholars have attached importance to them.

However, there are many uncertain phenomena which cannot be exactly measured by linear expectations.

Let S be a subset of all convex expectations containing all linear expectations.

Additivity has been generally regarded as a fairly natural assumption, so the classical probability theorems have always been considered under additive probabilities and the linear expectations.

Jia [7] studied the minimal members of sublinear expectations and their related properties, established the relationship between linear expectations and the minimal members of sublinear expectations, and obtained the so-called sandwich theorem for sublinear expectations and superlinear expectations.

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Many powerful inequations and conventional methods for linear expectation and probabilities are no longer valid, the study of limit theorems under sub-linear expectation becomes much more challenging.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