Sentence examples for by a linear expectation from inspiring English sources

The variance is: Variance includes extra variation due to equating a mixture by a linear expectation.

By Proposition 3.1, for a given concave expectation (mathcal{E}_{0}), there exists a linear expectation (E_{1} in S^{mathrm{l}}) such that (E_{1} geq mathcal{E}_{0}).

Let E be 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.

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

We prove that, for a subset S of all convex expectations containing all linear expectations, (mathcal{E}) is a minimal member of S if and only if (mathcal{E}) is a linear expectation.

Kurzweil: Because if I looked at the current situation, and then applied a linear expectation to it, and that is our intuition.

It says that (2) remains true when the expectation E is replaced by a sub-linear expectation (hat {mathbb {E}}) if {X n ;n≥1} are independent and identically distributed under (hat {mathbb {E}}), i.e., frac{S_{n}}{sqrt{n}}overset{d}rightarrow xi~text{under}~hat{mathbb{E}}, (5).

On the other side, in the classical stochastic optimal control and differential game theory, the performance criterion is described by the linear expectation (mathbb{E}).

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