2 мар. 2013 г. · The σ-algebra generated by E(X∣G), like any σ-algebra generated by a random variable, must be countably generated. So it cannot be any sub σ-algebra of G.

1 дек. 2012 г. · The conditional expectation over the trivial sigma field would be the Expectation of the random variable.

22 окт. 2015 г. · I can try to explain what I understand, what conditional expectation tries to accomplish (let's say we work on (Ω,A,P).

3 июн. 2022 г. · Let X be a mean-zero random variable on a probability space (Ω,F,P) and let G,H be two independent sub-sigma algebras. Then E(X∣σ(G∪H))=E(X∣G)+E(

18 апр. 2013 г. · If you're willing to assume that σ(σ(X)∪H) is independent of σ(G) and that X is integrable, then the assertion is indeed true.

7 июн. 2022 г. · Let's consider a probability space (Ω,F,P). Kolmogorov's definition of conditional expectation needs a sub-sigma-algebra of F as a condition.

18 сент. 2024 г. · The σ algebra is a collection of all events we can condition on. This would mean that E(X|σ(Y)) is a function of σ(Y)→R.

3 апр. 2018 г. · To calculate this let me state some facts about conditional expectation: It holds for a random variable H. If Z is a G measurable random ...

5 февр. 2021 г. · By the definition of conditional expectation, the constant value taken on Ai by EP(X|G) is the expected value of X on Ai, namely EP(X|Ai):=EP(X1 ...

29 дек. 2018 г. · Assume that B1 and B2 are two σ-sub-algebras of A such that E[X|Bi]=0 for i=1,2. I would expect that it now holds that E[X|σ ...