A Prophet Inequality for Independent Random Variables with Finite Variances
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Author(s)
Kennedy, D. P.
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Abstract
It is demonstrated that for each n \ge 2 there exists a universal constant, c_n, such
that for any sequence of independent random variables {X_r, r \ge 1} with finite variances,
E[max_{1\le i\le n} X_i] - sup_T EX_T \le c_n\sqrt{n - 1} max_{1\le i\le n}\sqrt{Var (X_i)}, where the supremum is
over all stopping times T, 1\le T \le n. Furthermore, c_n\le 1/2 and lim inf_{n\to\infty} c_n 0:439485 ....
Sponsor
NSF grant DMS 92-09586
Date
1995-09
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Text
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Pre-print