Let ck be the smallest sigma-algebra for which uj is, Basic Statistics

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Let ck be the smallest sigma-algebra for which uj is

Let Y be a random variable independent of all the X j , with E |Y | <>∞. Let Uj := Y + Tj for j = -1, -2,... . Let Ck be the smallest σ-algebra for which Uj is measurable for all j ≤ k. Show that {Uk, Ck }k≤-1 is a reversed martingale and find its limit as k → -∞. Let C-∞ := nk≤-1 Ck . Is Y equal a.s. to a variable measurable for C-∞?

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Basic Statistics: Let ck be the smallest sigma-algebra for which uj is

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