Two main conceptual leaps here are: 1) we condition with respect to a σ-algebra, and 2) we view the conditional expectation itself as a random variable. Before ...

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. What happens if you take conditional expectation on trivial ... Conditional expectation with respect to a σ-algebra Conditional expectation on more than one sigma-algebra Conditional Expectation of X with respect to a σ-algebra G Другие результаты с сайта math.stackexchange.com

18 авг. 2016 г. · One way to think about conditional expectation is as a projection onto the σ-algebra G. enter image description here (from Wikimedia commons). How to compute conditional expectations with respect to a ... How to understand conditional expectation w.r.t sigma-algebra Precise Definition of E[X∣σ(A)] Conditional Expectation of ... Exact meaning of conditional expectation E[X|F] - Cross Validated Другие результаты с сайта stats.stackexchange.com

It provides the closest approximation to a random variable X if we restrict to random variables Y measurable with respect so some courser sigma algebra.

In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated

Defining conditional probability with respect to a sigma-algebra allows us to to condition on zero-probability events. Discover how and why. Motivation · Roadmap · Conditioning with respect to...

8 нояб. 2017 г. · We can condition on events of positive probability, or on the σ-algebra generated by a random variable. In Radon spaces (which include Rd and ...

Conditional expectation with respect to a -Algebra as a random variable. 2 Conditional expectation with respect to a σ-Algebra. 2.1 Why do we need all that ...

15 окт. 2015 г. · Is conditional expectation with respect to two sigma algebra exchangeable? (Ω,F,P) is a probability space. X is a r.v. defined on it, and G1,G2 ...

The conditional expectation ErX | Gs is supposed to be the “best” prediction one can make about X if we only have the information contained in σ-algebra G.