Bennett Eisenberg
Professor of Mathematics
Department of Mathematics #14
Lehigh University
Bethlehem, PA 18015
Telephone: Office: 610-758-3736 Home: 610-865-5289
e-mail: BE01@Lehigh.edu
Employment history:
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Lehigh University 1972-present
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University of New Mexico 1970-1972
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Cornell University 1967-1970
Education:
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Ph.D. 1968, M.I.T.
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A.B. 1964, Dartmouth
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Coolidge High School, Washington, D.C., 1960
Research areas: Gaussian processes, ergodic theory, stationary processes,
sequential statistical tests, epidemiology, record values, geometric optimization
and geometric probability, probability theory.
Selected publications categorized according to research area.
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Gaussian processes:
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Translating Gaussian Processes, Ann. Math. Stat. 1970
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Baxter's Theorem and Varberg's Conjecture. Pacific J. Math. 1972
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The Equivalence Singularity Problem for Gaussian Signals in Gaussian Noise.
IEEE
Trans. on Information Theory. 1986
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Ergodic theory:
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Generalized Summing Sequences and the Mean Ergodic Theorem, Proc. Amer.
Math. Soc. 1974 (with J. Blum)
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Ergodic Theory and the Measure of Sets in the Bohr Group, Acta Sci.
Math. (Szeged) 1973 (with J. Blum and L-S. Hahn.
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Ergodic Theorems for Mixing Transformation Groups. Rocky Mt. J.
of
Math. 1979 (with J. Blum)
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Stationary Processes:
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Conditions for Metric Transitivity for Stationary Gaussian Processes on
Groups. Ann. Math. Stat. 1972. (with J. Blum)
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Linear Estimation of Regression Coefficients. Quarterly of Applied
Math. 1974. (with R. Adenstedt)
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The Law of Large Numbers for Subsequences of a Stationary Process. Annals
of Prob. 1975 (with J. Blum)
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Sequential statistical tests:
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Non-Optimality of Likelihood Ratio Tests in the Sequential Detection of
Signals in Gaussian Noise. Statistical Decision Theory. 1971.
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Properties of Generalized Sequential Probability Ratio Tests. Ann. of
Stat. 1976. (with B. Ghosh and G. Simons)
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On Weak Admissibility of Tests. Ann. of Stat. 1978. (with G. Simons
)
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On the Sample Size of Curtailed Tests. Comm. in Stat. 1981. (with
B. Ghosh)
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The Asymptotic Solution of the Kiefer-Weiss Problem. SequentialAnalysis.
1982.
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Multihypothesis Problems. Handbook of Sequential Analysis. 1991.
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One-sided SPRT's which Hit the Boundary. Sequential Analysis. 1995.
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Epidemiology.
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The Number of Partners and the Probability of HIV Infection. Stat. i
n Medicine. 1989.
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The Effect of Variable Infectivity on the Risk of HIV Infection. Stat.
in Medicine. 1990.
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Record Values.
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The Asymptotic Probability of a Tie for First Place. Ann. of Applied
Prob. 1993. (with G. Strang and G. Stengle)
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A Necessary and Sufficient Condition for the Existence of the Limiting
Probability of a Tie for First Place. Stat. and Prob. Letters.
1995.
(with Y. Baryshnikov and G. Stengle)
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Minimizing the Probability of a Tie for First Place. J. of Math.Analysis
and its Applic. 1996. (with G. Stengle)
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Geometric Optimization and Geometric Probability
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Optimal Locations. College Math. J. 1992. (with S. Khabbaz)
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Random Triangles in n-Dimensions. Amer. Math. Monthly. 1996. (with
R. Sullivan)
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Crofton's Differential Equation. Amer. Math. Monthly. 2000
(with R. Sullivan)
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Probability Theory.
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Another Look at Korovkin's Theorem. J. of Approx. Theory. 1976.
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Uniform Convergence of Distribution Functions. Proc. Amer. Math.Soc.
1983.
(with Shixin Gan)
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Positive Martingales and their Induced Measures. Proc. Amer. Math. Soc.
1983.
(with Shixin Gan)
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Independent Events in a Discrete Uniform Probability Space. TheAmer.
Statistician. 1987. (with B. Ghosh)
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Independent Events and Independent Experiments. Proc. Amer. Math.Soc.
1993.
(with Y. Baryshnikov)
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What is the Margin of Error of a Poll? College Math. J. 1997
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How Much Should You Pay for a Derivative? College Math. J.
1998.