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- José Enrique Figueroa-López, Christian Houdré, +6 authors Hamed Marrofi
- 2003

ACKNOWLEDGEMENTS There have been many individuals in my life without whom the completion of this work would not have been possible. It is my intension to briefly recognize their contribution to my personal and professional life. I would like to thank my advisor, Dr. Christian Houdré, for his support and orientation through all my studies at Georgia Tech. In… (More)

Suppose fix,... ,fin are nonatomic probability measures on the same measurable space (S, S). Then there exists a measurable partition isi}"=i of 5 such that Pi(Si) > (n + 1 M)'1 for a11 i l,...,n, where M is the total mass of V?=i ßi (tne smallest measure majorizing each m). This inequality is the best possible for the functional M, and sharpens and… (More)

(1/4)(b-a), and this bound is best possible. Probabilis-tically, this says that if a prophet (player with complete foresight) makes a side payment of (b-a)/8 to a gambler (player using nonanticipating stop rules), the game becomes at least fair for the gambler.

- Robert P. Kertz
- Math. Oper. Res.
- 1982

- Hill I, Robert P Kertz
- 2006

Implicitly defined (and easily approximated) universal constants 1.1 < an random variables and if Tn is the set of stop rules for Xl, "', Xn, then E(max{Xl , • • • ,Xn}) ~ an sup {EX, : tE Tn}, and the bound an is best possible. Similar universal constants 0 < bn < Y. are found so that if the {Xi} are i.i.d. random variables taking values only in [a, b),… (More)

- Robert P Kertz
- 2007

A class of generalized convex functions, the hyperbolic{concave functions, is deened, and used to characterize the collection of Hardy{ Littlewood maximal functions. These maximal functions and the probability measures associated with these maximal functions, the maximal probability measures, are used in representations and inequalities within martingale… (More)

If X"0, Xx_ is an arbitrarily-dependent sequence of random variables taking values in [0,1] and if V X C= UQ. »=i As a special case, if A"0, X,,... is a martingale with EX0 x, then £(max7tí " X) =c x + nx(\ x'/n) and £(sup " Xlt) « x x\n x, and both inequalities are sharp. 1. Introduction. The subject of this paper is comparisons between the expected… (More)

- Robert Kertz, Sarah Quinn, Gareth Rose, Kevin Strotz, Penny Sun
- 2011

In the modern electronic instrument market, drum machines are often far too expensive and complex for operation by the everyday user. This project addressed this shortcoming by designing and building a user-friendly and cost-effective drum machine with an Atmel ATmega2560 microcontroller running the Arduino platform, a Voice Shield chip, and a limited… (More)

- Hee Jung Sim, Paul M. Griffin, Robert P. Kertz, Joel Sokol, Qiong Wang
- 2005

ACKNOWLEDGEMENTS During the preparation of this thesis, there have been many people whose prayer, support, and encouragement have contributed to its accomplishment. First of all, I would like to thank my advisor, Professor Shijie Deng. His thoughtful comments, helpful suggestions, and consistent guidance made the preparation of this thesis an invaluable… (More)

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