On the worst conditional expectation

CONDITIONAL EXPECTATION IN THE KOPKA'S D-POSETS

The notion of a $D$-poset was introduced in a connection withquantum mechanical models. In this paper, we introduce theconditional expectation of  random variables on theK^{o}pka's $D$-Poset and prove the basic properties ofconditional expectation on this  structure.

Conditional Expectation

Let μ and λ be two positive bounded measures on the same meaurable space (Ω,F). We call μ and λ equivalent, and write μ ≡ λ, if they have the same null sets— so, if they were probability measures, the notion of “a.s.” would be the same for both. More generally, we call λ absolutely continuous (AC) w.r.t. μ, and write λ μ, if μ(A) = 0 implies λ(A) = 0, i.e., if every μ-null set is also λ-null. W...

Independence Tests based on the Conditional Expectation

In this paper we propose a new procedure for testing independence of random variables, which is based on the conditional expectation. As it is well known, the behaviour of the conditional expectation may determine a necessary condition for stochastic independence, that is, the so called mean independence. We provide a necessary and sufficient condition for independence in terms of conditional e...

Conditional expectation

On the stability problem for conditional expectation

The behavior of the conditional expectation E{X I Y) under a small perturbation Z of the conditioning random variable Y is analyzed. We show that if Y and Z are independent then E(XIY + EZ) converges to E{XIY) in mean as E --* 0 for all integrable X, provided the distribution of Y is absolutely continuous. We also show that the limit is E{X 1 Y, Z} rather than E(X 1 Y}, i.e., there is no stabil...