(Georgia Institute of Technology, 1995-09)
Kennedy, D. P.; Kertz, Robert P.
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 ....