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).

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.

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.

9 апр. 2016 г. · The conditional expectation must be G-measurable, by definition. So if X is not, the equality does not hold. Take the example of my answer. You ...

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 апр. 2013 г. · So for a finite σ-algebra the classical conditional expectation can be described as the only G-measurable function that satisfies the condition ...

9 сент. 2015 г. · Conditional expectation given an event is equivalent to conditional expectation given the sigma algebra generated by the event. This problem is ...

27 июл. 2017 г. · The following are the definitions of conditional expectation and conditional probability, could you fit your case in?

5 февр. 2019 г. · Is there a choice of a σ-algebra which makes the conditional expectation of an random-variable X∈L1P(F,P), on a probability space (Ω,F,P) equal ...