My Math Forum Weak convergence of the sum of dependent variables question

 December 13th, 2011, 02:15 PM #1 Newbie   Joined: Dec 2011 Posts: 1 Thanks: 0 Weak convergence of the sum of dependent variables question Hi guys, Problem: Let {Xn},{Yn} - real-valued random variables. {Xn}->{X} - weakly; {Yn}->{Y} weakly. Assume that Xn and Yn - independent for all n and that X and Y - are independent. Show that {Xn+Yn}->{X+Y} weakly. This can be shown using Levy's theorem and characteristic functions. Question: If independence does not hold, can you construct a counterexample? I appreciate any help in advance.

 Tags convergence, dependent, question, sum, variables, weak

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