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Convergence of non increasing sequence of random number

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ensei
#1
Dec31-12, 01:58 AM
P: 2
I have a non-increasing sequence of random variables [itex] \{Y_n\}[/itex] which is bounded below by a constant [itex]c[/itex], [itex]\forall \omega \in \Omega[/itex]. i.e [itex]\forall \omega \in \Omega[/itex], [itex]Y_n \geq c[/itex], [itex]\forall n[/itex]. Is it true that the sequence will converge to [itex]c[/itex] almost surely?

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mfb
#2
Dec31-12, 10:49 AM
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Hint: If c is such a constant, what about c-1?
ensei
#3
Dec31-12, 06:45 PM
P: 2
Quote Quote by mfb View Post
Hint: If c is such a constant, what about c-1?
All the elements of the sequence are bounded below by c. So, I am not sure what are you trying to say. can you please elaborate?

HallsofIvy
#4
Jan1-13, 04:24 AM
Math
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PF Gold
P: 39,691
Convergence of non increasing sequence of random number

His point is that if the set is bounded below by c, it is also bounded below by c-1 or, for that matter any number less than c. Just saying "bounded below by c" does NOT tell you very much. You seem to be confusing "lower bound" with "greatest lower bound".


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