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- José Enrique Figueroa-López, Christian Houdré, Robert P Kertz, Marcus C Spruill, Richard Serfozo, Isye
- 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)

This paper surveys the origin and development of what has come to be known as "prophet inequalities" in optimal stopping theory. Included is a review of all published work to date on these problems, in cl uding extensions and variations, descriptions and examples of the main proof techniques, and a list of a number of basic open problems.

Date Approved by Chairman: iii Dedication to my parents and family iv Acknowledgment I would like to express my sincere gratitude to everyone who has made it possible for me to achieve my goals and finish my degree. First and foremost I am grateful to my advisor, Professor Jim Dai, for introducing me to reflecting Brownian motions and their applications in… (More)

- 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)

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 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)

- 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)