Interval-dividing processes |
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| Authors: | Sam Gutmann |
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| Institution: | (1) Dept. of Mathematics, Northeastern University, 360 Huntington Avenue, 02115 Boston, MA, USA |
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| Abstract: | Summary If
and
then P(n
–1· (Y
1)+ +(Y
n
)] converges to cnts. law on R
1) = P(n
–1·(Y
1)++(Y
n
)] converges to a cnts. law on R
1). Thus if
,n then n
–1(X
1)+...+(X
n
)] converges a.s. The main result here generalizes this: Let X
(1)
n
, X
(2)
n
,..., X
(n)
n
be the order statistics associated with X
1, X
2,,X
n. Define random variables Z
1,Z
2, by {Z
n
=i}={X
n
=X
(i)
n
}. Then if Z
1,Z
2,Z
3, are independent and P(Zn i)i/n, and {X
i} is bounded, n
–1·(X
1)++(X
n)] converges a.s. |
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| Keywords: | |
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