of Mathematics #14
Bethlehem, PA 18015
Telephone: Office: 610-758-3736 Home: 610-865-5289
- Lehigh University 1972-present
- University of New Mexico 1970-1972
- Cornell University 1967-1970
- Ph.D. 1968, M.I.T.
- A.B. 1964, Dartmouth College
- Coolidge High School, Washington, D.C., 1960
areas: Gaussian processes, ergodic theory, stationary
processes, sequential statistical tests, epidemiology, record values, geometry and geometric probability, probability theory.
Selected publications categorized according to research area.
- Gaussian processes:
- The Relation of the
Equivalence Conditions for Brownian Motion to
the Equivalence Conditions for Certain Stationary Processes, Ann.
Math. Stat. 1969.
- Translating Gaussian
Processes, Ann. Math. Stat. 1970.
- Baxter's Theorem and Varberg's Conjecture. Pacific J. Math. 1972.
- The Equivalence
Singularity Problem for Gaussian Signals in Gaussian Noise. IEEE
Trans. on Information Theory. 1986.
- Ergodic theory:
- Generalized Summing
Sequences and the Mean Ergodic Theorem, Proc.
Amer. Math. Soc. 1974 (with J. Blum).
- Ergodic Theory and the Measure
of Sets in the Bohr Group, Acta Sci.
Math. (Szeged) 1973 (with J. Blum and L-S. Hahn).
- Ergodic Theorems for Mixing
Transformation Groups. Rocky Mt. J. of Math. 1979 (with J.
- Stationary Processes:
- Conditions for Metric Transitivity
for Stationary Gaussian Processes on Groups. Ann. Math. Stat. 1972
(with J. Blum).
- A Note on Metric
Transitivity for Stationary Gaussian Processes on Groups. Ann. Math.
Stat. 1972 (with J. Blum).
- Linear Estimation of
Regression Coefficients. Quarterly of Applied Math. 1974 (with R. Adenstedt).
- The Law of Large
Numbers for Subsequences of a Stationary Process. Annals of Prob.
1975 (with J. Blum).
- A Note on Random
Measures and Moving Averages on Non-Discrete Groups. Ann. Math. Stat. 1973
(with J. Blum).
- Spectral Properties of
Processes Derived from Stationary Gaussian Sequences. Stoch.
Proc. and their Appl. 1974.
- Prediction Theory and Ergodic Spectral Decompositions, Ann. of Prob. 1976
(with J. Blum).
- Sequential statistical tests:
- Non-Optimality of
Likelihood Ratio Tests in the Sequential Detection of Signals in Gaussian
Noise. Statistical Decision Theory. 1971.
- Properties of
Generalized Sequential Probability Ratio Tests. Ann. of Stat. 1976 (with B. Ghosh and G.
- On Weak Admissibility
of Tests. Ann. of Stat. 1978 (with
G. Simons ).
- The Likelihood Ratio
and its Applications to Sequential Analysis. Ann. of
Stat. 1980 (with B. Ghosh).
- Curtailed and Uniformly
Most Powerful Sequential Tests. Ann. of Stat. 1980 (with B. Ghosh).
- On the Sample Size of
Curtailed Tests. Comm. in Stat.-Theory and Methods. 1981 (with B. Ghosh).
- The Asymptotic Solution
of the Kiefer-Weiss Problem. Sequential Analysis. 1982.
- Multihypothesis Problems. Handbook
of Sequential Analysis. 1991.
- The Sequential
Probability Ratio Test. Handbook of Sequential Analysis. 1991.
- One-sided SPRT's which
Hit the Boundary. Sequential Analysis. 1995
- Average Sample Number, Kluwer
Encyclopedia of Mathematics, 2002.
- Sequential Probability
Ratio Test, Kluwer Encyclopedia
of Mathematics, 2002.
- Discussion on
"Likelihood Ratio Identities and Their Application in Sequential
Analysis" by T.L. Lai, Sequential Analysis, 2004.
- Discussion on
"Life and Work of Bhaskar Kumar Ghosh" by Pranab Kumar
Sen, Sequential Analysis, 2010 (with W.
- The Number of Partners
and the Probability of HIV Infection. Stat. in Medicine. 1989.
- The Effect of Variable
Infectivity on the Risk of HIV Infection. Stat. in Medicine. 1990.
- Record Values.
- The Asymptotic
Probability of a Tie for First Place. Ann. of Applied Prob. 1993
(with G. Strang and G. Stengle).
- 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).
- Minimizing the
Probability of a Tie for First Place. J. of Math. Analysis and its Applic. 1996 (with
- On the Expectation of
the Maximum of I I D Geometric Random
Variables, Stat. and Prob. Letters. 2008.
- The Number of
Players Tied for the Record, Stat.
and Prob. Letters. 2009.
- Geometry and Geometric Probability
- Optimal Locations. College
Math. J. 1992
(with S. Khabbaz).
- Random Triangles in
n-Dimensions. Amer. Math. Monthly. 1996 (with
- Crofton's Differential
Equation. Amer. Math. Monthly. 2000 (with R. Sullivan).
- The Fundamental Theorem
of Calculus in Two Dimensions, Amer.
Math. Monthly. 2002 (with R. Sullivan).
- Surfaces of Revolution
in Four Dimensions, Math.
- A Modification of
Sylvester’s Four Point Problem, Math.
- Probability Theory.
- Another Look at Korovkin's Theorem. J. of Approx. Theory. 1976.
- Uniform Convergence of
Distribution Functions. Proc. Amer. Math. Soc. 1983 (with Shixin Gan).
- Positive Martingales
and their Induced Measures. Proc. Amer. Math. Soc. 1983 (with Shixin Gan).
- Independent Events in a
Discrete Uniform Probability Space. The Amer. Statistician. 1987
(with B. Ghosh).
- A Variation of a
Theorem of Sparre-Andersen, Stat. and Prob.
- Independent Variables
with Independent Sum and Difference. J. of Multivariate Anal. 1993
(with Y. Baryshnikov and W. Stadje).
- Independent Events and
Independent Experiments. Proc. Amer. Math.Soc.
1993 (with Y. Baryshnikov).
- What is the Margin of
Error of a Poll? College Math. J. 1997
- How Much Should You Pay
for a Derivative? College Math. J. 1998.
- Generalizations of
Markov's Inequality, Stat. and Prob. Letters. 2001 (with B. Ghosh).
- Why is the Sum of
Independent Normal Random Variables Normal? Math. Magazine, 2008
(with R. Sullivan).