
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
December 13th, 2011, 03:15 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}  realvalued 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 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Weak Convergence Question  PeterPan  Real Analysis  1  January 21st, 2014 03:16 PM 
Weak convergence in compact embedding  John Do  Real Analysis  2  January 13th, 2014 04:55 AM 
Very Weak In Maths  rohit786  Academic Guidance  13  February 8th, 2013 08:26 PM 
Almost sure convergence of sequences of random variables?  boot20  Advanced Statistics  3  July 9th, 2010 02:20 PM 
Weak Convergence  VladP  Real Analysis  0  October 22nd, 2009 12:57 PM 