[分析] conditional expectation
Let Y be L^2(ω,G,P),
Suppose E(Y^2|X) = X^2 and E(Y|X) = X.
Show that Y = X almost surely.
這裡的 conditional expectation 定義方式是
the unique element E(Y|X) in L^2(ω,sigma(X),P),
such that E(YZ)=E(E(Y|X)Z) for all Z in L^2(ω,sigma(X),P).
感謝大家~
--
※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 49.218.6.71
※ 文章網址: https://www.ptt.cc/bbs/Math/M.1457175692.A.D42.html
※ 編輯: simon81921 (49.218.6.71), 03/05/2016 19:04:50
推
03/06 06:41, , 1F
03/06 06:41, 1F
→
03/06 18:28, , 2F
03/06 18:28, 2F
→
03/06 18:28, , 3F
03/06 18:28, 3F