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December, 1977 An Improved Upper Bound for Standard $p$-Functions
V. M. Joshi
Ann. Probab. 5(6): 999-1003 (December, 1977). DOI: 10.1214/aop/1176995666


For standard $p$-functions, an upper bound for $M = p(1)$, for a given value $m$ of $m(p) = \min\{p(t), 0 < t \leqq 1\}$, was proved in a previous paper by the author. The bound implied that $\nu_0 \leqq .590, \nu_0$ being the constant defined by $$I_M = \inf\{m(p)|p(1) = M\},\quad \nu_0 = \inf\{M|I_M > 0\},$$ in which $p$ varies over the class of standard $p$-functions. In the present paper both of these upper bounds are sharpened by a refinement of the argument, the limit for $\nu_0$ being reduced to .560.


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V. M. Joshi. "An Improved Upper Bound for Standard $p$-Functions." Ann. Probab. 5 (6) 999 - 1003, December, 1977.


Published: December, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0371.60081
MathSciNet: MR445618
Digital Object Identifier: 10.1214/aop/1176995666

Primary: 60J10
Secondary: 60J25 , 60K05

Keywords: Kingman inequalities , regenerative phenomena , Standard $p$-functions

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 6 • December, 1977
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