Summary
Suppose X 1,X 2,...,Xn are independent non-negative random variables with finite positive expectations. Let T n denote the stop rules for X 1,...,X n. The main result of this paper is that E(max{X 1,...,X n }) <2 sup{EX t :tεT n }. The proof given is constructive, and sharpens the corresponding weak inequalities of Krengel and Sucheston and of Garling.
Bibliography
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Partially supported by AFOSR Grant F49620-79-C-0123
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Hill, T.P., Kertz, R.P. Ratio comparisons of supremum and stop rule expectations. Z. Wahrscheinlichkeitstheorie verw Gebiete 56, 283–285 (1981). https://doi.org/10.1007/BF00535745
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DOI: https://doi.org/10.1007/BF00535745
Keywords
- Stochastic Process
- Probability Theory
- Mathematical Biology
- Positive Expectation
- Ratio Comparison