Hi guys,

Any chance anyone could help me think of a function as in probability but it does not convergence almost surely nor in ?

Thanks in advance!

YChana

- Apr 13th 2011, 05:30 AMychanaConvergence in probability but no convergence in L^p nor A.S.
Hi guys,

Any chance anyone could help me think of a function as in probability but it does not convergence almost surely nor in ?

Thanks in advance!

YChana - Apr 13th 2011, 07:58 AMMoo
Hello,

If I'm not mistaking, you can have a look at sequence of independent rv's where

It does converge in probability, but doesn't converge in Lp. As for the almost sure converge, we'll have to use Borel-Cantelli (look here for proving that part) - Apr 16th 2011, 12:19 AMmatheagle
how about P(X_n=n)=1/n and P(X_n=0)=1-1/n

- Apr 16th 2011, 06:17 AMMoo