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Probality problem
Posted: April 19th, 2013, 8:13 am
by fmfreshman
Suppose random variable X converges to Y in L2 spaceHow can we prove the expectation E(e^X-e^Y) converges to zero, any ideas?
Probality problem
Posted: April 19th, 2013, 2:30 pm
by deimanteR
This does not follow. You need extra conditions and can try using the dominated convergence or maybe the sequence is uniformly integrable?
Probality problem
Posted: April 29th, 2013, 2:00 pm
by EscapeArtist999
QuoteOriginally posted by: deimanteRThis does not follow. You need extra conditions and can try using the dominated convergence or maybe the sequence is uniformly integrable?I think if lim_(n -> infty) E[exp(2*max(X_n,Y))] < infty you can use the mean value theorem and cauchy shwartz (in addition to L2) to get convergence... this is b=very simplistic... sure there s a better soln - but a first stab.