conditional expectation in the kopka's d-posets

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 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 states and independence in D-posets

Conditional probability plays a basic role in the classical probability theory. Some of the most important areas of the theory such as martingales, stochastic processes rely heavily of this concept. Conditional probabilities on a classical measurable space are studied in several different ways, but result in equivalent theories. The classical probability theory does not describe the causality m...

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...

Conditional expectation

Lecture 10 Conditional Expectation

We say that P[A|B] the conditional probability of A, given B. It is important to note that the condition P[B] > 0 is crucial. When X and Y are random variables defined on the same probability space, we often want to give a meaning to the expression P[X ∈ A|Y = y], even though it is usually the case that P[Y = y] = 0. When the random vector (X, Y) admits a joint density fX,Y(x, y), and fY(y) > 0...