Strong consistency of the mean on randomly deleted sets |
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| Authors: | Mark D Rothmann Ralph P Russo |
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| Institution: | (1) School of Mathematics, Georgia Institute of Technology, 30332 Atlanta, Georgia;(2) Department of Statistics, University of Iowa, 52242 Iowa City, Iowa |
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| Abstract: | Suppose 0 t
1<t
2<... are fixed points in time. At timet
k
, a unit with magnitudeX
k
and lifetimeL
k
enters a population or is placed into a system. Suppose that theX
k
's are i.i.d. withEX
1= , theL
k
's are i.i.d., and that theX
k
's andL
k
's are independent. In this paper we find conditions under which the continuous time process Avr{X
k
:t
k
t<t
k
+L
k
} is almost surely convergent to . We also demonstrate the sharpness of these conditions. |
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| Keywords: | Strong law of large numbers sample means random deletion |
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