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May 2, 2013 at 2:42 comment added bryan Makes sense. A simple counterexample to the first question would be $v_1(t) = X$, and $v_2(t) = Y$ for $t < 1, v_2(t) = Z$ for $t >= 1$ with $X, Y, Z$ all being independent standard normals. $v_1$ and $v_2$ are equal in distribution but their integrals are not. Thank you very much for your help!
May 2, 2013 at 2:36 vote accept bryan
May 1, 2013 at 18:06 history answered Carlo Beenakker CC BY-SA 3.0