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:**

- Lehigh University 1972-present
- University of New Mexico 1970-1972
- Cornell University 1967-1970

**Education:**

- Ph.D. 1968, M.I.T.
- A.B. 1964, Dartmouth College
- Coolidge High School, Washington, D.C., 1960

Research
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. Blum). **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. Simons). - 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. Huang). *Epidemiology.*- 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 G. Stengle). - 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 R. Sullivan). - 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**. Magazine,*2004. - A Modification of
Sylvester’s Four Point Problem,
*Math. Magazine,*2011. **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. Letters.*1992. - 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).