Topic profile page for Almost sure.
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Topic "Almost sure" was discussed 10,420 times on 2,328 sites in last 3 months
Started 1 week, 1 day ago (2009-11-24 20:35:33)
by Brad S
Yup, I'm almost sure FFGO's claims will end up either being in the NMGL stable through default or that FFGO's interest in the claims will be handed over to the "third parties" as payment of the dept owed to them.
Started 1 week, 2 days ago (2009-11-23 20:40:00)
by kingwinner
1. The problem statement, all variables and given/known data "Almost sure convergence" always implies "convergence in probability", but the converse is NOT true. Thus, there exists a sequence of random variables Y n such that Y n ->0 in probability, but Y n does not converge to 0 almost surely. 2. Relevant equations N/A 3. The attempt...
Started 1 week, 2 days ago (2009-11-23 20:37:00)
by kingwinner
"Almost sure convergence" always implies "convergence in probability", but the converse is NOT true. Thus, there exists a sequence of random variables Y_n such that Y_n->0 in probability, but Y_n does not converge to 0 almost surely. I think this is possible if the Y's are independent, but still I can't think of an concrete example. What is of example of this happening? Any help ...
Started 1 week, 3 days ago (2009-11-22 10:31:00)
by Amelia
Let Y_n be a simple symmetric random walk on the integers Z, starting in state 0. Define X_n to be 1 if Y_n=0 and 0 otherwise. I have already shown that X_n converges in probability to 0 as n tends to infinity. But how can I show that X_n does NOT converge almost surely to 0 as n tends to infinity? I know that Y_n is recurrent (in fact, null recurrent) but how can I use this ...
Started 6 days, 10 hours ago (2009-11-26 17:29:12)
by benbarba
It's almost a sure thing that all the U.S. stocks will crash tomorrow. Based on the average worlds stocks that were open when the news broke, the major indices fell on average 3%. That means the Dow will fall around 400 points tomorrow and Monday. Here is a Market Watch link that tells more about it: http://www.marketwatch.com/story/dubai-woes-roil-f inancial-markets-2009-11-26
Started 6 days, 8 hours ago (2009-11-26 19:29:37)
by benbarba
It's almost a sure thing that all the U.S. stocks will crash tomorrow. Based on the average worlds stocks that were open when the news broke, the major indices fell on average 3%. That means the Dow will fall around 400 points tomorrow and Monday. Here is a Market Watch link that tells more about it: http://www.marketwatch.com/story/dubai-woes-roil-f inancial-markets-2009-11-26 There is also a ...
Started 6 days, 18 hours ago (2009-11-26 10:23:00)
by kingwinner
Quote: Originally Posted by Martingale since P(X_n=1)=1/n by the B-C Lemma we know that [X_n=1 i.o.] if this is the case how could X_n converge almost surely to zero? By part (ii) of B-C lemma, since ∑ P(X_n=1)= ∑1/n = ∞, this implies that P(X_n=1 io)=1, but WHY does this imply that Xn does not converge ...
If you want an example, think about playing a game where the nth time play you win 1 dollar with probability 1/n. If you play an infinite number of times the expectation value of your winning amount is infinite. Doesn't that mean that almost surely, you won an infinite number of times? That's not a proof of anything, but is that what you are asking?
