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Conditional expectation with respect to a $\sigma$-algebra
Could someone explain what it is that we are intuitively trying to achieve with the definition? Having read the definition I could do the problems in the section of my book, but I still have no...
View ArticleAnswer by martini for Conditional expectation with respect to a $\sigma$-algebra
I can try to explain what I understand, what conditional expectation tries to accomplish (let's say we work on $(\Omega, \mathscr A, \mathbf P)$.(1) The "information" carried by a $\sigma$-algebra...
View ArticleAnswer by bakula for Conditional expectation with respect to a $\sigma$-algebra
One can think of the "information carried by a $\sigma$-algebra" as a measure of "roughness" of the events we are considering. For example, think of the probability space modelling the outcome of...
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