Stopping rules forx
n/n and related problems |
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| Authors: | Y S Chow A Dvoretzky |
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| Institution: | (1) Stanford University, USA;(2) The Hebrew University of Jerusalem, Israel;(3) Columbia University, USA |
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| Abstract: | The following results illustrate the problems with which this note deals. Letx
n (n=1, 2, ...) be non-negative, independent, identically distributed random variables, letβ>1 andEx
1
β
<∞. Then there exists a stopping ruleτ withP{τ<∞}=1, which maximizesE x
t/t among all stopping rulest. Moreover, the same rule maximizesE max (x
1, ...,x
t)/t andE max (x
1,..,x
τ)/τ=Ex
τ/τ
Research supported in part by Grant GP-5705 of the National Science Foundation, USA. |
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| Keywords: | |
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