Stamatis was born on July 8, 1943 in Athens, Greece. He grew up in Greece and graduated from the National Technical University of Athens in 1966 with a B.S. in Electrical and Mechanical Engineering. In 1966 he came to the Electrical Engineering Department at Princeton University for his doctoral studies, and he graduated in 1968.He then joined the faculty of the Statistics Department, University of North Carolina at Chapel Hill, where he remained until his untimely death.
His interest in random processes had been ignited in Princeton, and already in his Ph.D.dissertation he had obtained new orthogonal series and integral representations for harmonizable processes. It was only fitting that he would find a home in the Statistics Department at UNC where, for the past twenty-seven years, he made fundamental contributions to the areas of probability theory, random processes, estimation theory, communication systems, and signal analysis and processing.
Stamatis is internationally known for his major contributions to the theory of stable processes. These processes have stable distributions with index 0 < a < 2 (a = 2 is the Gaussian case). For, 0 < a < 2, such processes have heavier tails than the Gaussian process and are thus more appropriate for models with outliers. In a series of twenty-seven papers beginning in 1980, Stamatis thoroughly studied the path properties, ergodicity, Wold decomposition, Markovian, and prediction properties of stable processes. It turned out that, although non-Gaussian stable processes share some properties with Gaussian processes, they differ in terms of their ergodicity, their moving average and spectral representations, their prediction, and the detectability of sure signals embedded in them.
Stamatis also made fundamental contributions to the study of stochastic and multiple Wiener integrals. The well known results for the Wiener processes were extended to general Gaussian processes, and the associated stochastic calculus was developed. Stochastic integral representation and an orthogonal series expansion in terms of multiple Wiener integrals were obtained for every L2-functional of a Gaussian process. Applications to the identification of nonlinear systems with Gaussian input were given.
The problem of sampling designs has many applications to detection of sure signals in noise, filtering, and the estimation of regression coefficients. In these applications, one desires to estimate a weighted integral of a random process over a finite interval from observations at a finite number of properly selected sampling points, which may be deterministic or random. Stamatis obtained asymptotically optimal deterministic designs when the discrete-time estimators use simple non-optimal coefficients, and he showed that their asymptotic performance is identical to that of estimators that use optimal coefficients. This work is significant in practice because the latter estimators require knowledge of the covariance function of the process and involve covariance matrix inversions that may not be stable for large sample sizes. These sampling designs can dramatically outperform uniformly-spaced designs. He also investigated a variety of Monte Carlo integration schemes, including stratified and stratified/symmetrized sampling, and obtained their convergence properties. Applications to filtering, prediction, and detection problems were given.
In the area of second order random processes and linear functionals, Stamatis obtained new series representations for harmonizable processes, weakly continuous processes, and general second-order processes, valid over finite or infinite intervals, generalizing the classical Karhunen-Lo\`eve representation. He then applied the new representations to linear mean-square filtering.
Other areas to which Stamatis made significant contributions include bandlimited processes and sampling expansions, rate distortion theory, quantization and delta modulation, and, more recently, wavelet transforms and wavelet representations of stationary and nonstationary random processes.
During his career Stamatis received national and international recognition for his academic and scientific accomplishments. He was elected Fellow of the Institute of Mathematical Statistics in 1984 and Fellow of the IEEE in 1989. In 1987 he was awarded an honorary doctorate in Mathematics by the University of Athens, Greece.
He gave generously of his time to professional societies as an editor for several mathematical, statistical, and engineering journals.For fourteen years, beginning in 1976, he was a member of the editorial board of SIAM Journal of Applied Mathematics. From 1983 to 1986 he served as the Associate Editor for Stochastic Processes of the IEEE Transactions on Information Theory. From 1990 until the last few months of his life he was a member of the editorial boards of Advances in Applied Probability and Journal of Applied Probability.
From 1986 till 1993 Stamatis served with distinction as Chairman of the Department of Statistics, University of North Carolina at Chapel Hill. He was admired by his colleagues for his devotion, effectiveness, and fairness. During his tenure seven young statisticians were hired by the department. He was one of the founders and administrators of the Center of Stochastic Processes in the Department of Statistics, which was established in 1981 and was supported for many years by AFOSR. The Center, which has a national and international reputation, has been exceptionally active, attracting approximately eighteen visitors from around the globe each year.
Stamatis loved teaching. He was extraordinarily gifted in explaining the most complex material in probability theory and random processes to his students in a clear and understandable way. He was extremely popular among graduate students and supervised eleven Ph.D. students: Alan Lee (University of Auckland, New Zealand), Steel T. Huang, Hoi Ming Leung (Food and Drug Administration, Rockville, MD), Grady W. Miller, Carol Schoenfelder, Muhammad Habib (George Mason University, Fairfax, VA), Neil L. Gerr (Office of Naval Research, Washington, DC), Mauro Marques (University of Campinas, Brazil), Karim Benhenni (Universit\'e Pierre Mendes France, Grenoble, France), Wei Wu (University of Illinois, Urbana, IL), and Yingcai Su (University of Arizona, Tucson, AZ). He worked closely with his Ph.D. students, devoting countless hours to assisting them with technical details.
A true Mediterranean, Stamatis was very gregarious and people would seek his company at workshops and conferences. He was joyful and had a great sense of humor; his roaring laughter could be heard several offices down the hall. Stamatis was a warm, kind, gentle, and generous person with true decency and innate integrity. He was also a deeply caring friend, stepping in to help others in his characteristically discreet way. He was humble both regarding his intellectual achievements and moral qualities.
During the past twenty years, Stamatis often visited us at our home in La Jolla during the summer. His visits were wonderful occasions for collaborative work, fellowship, and fun. Stamatis will always be remembered for his gracious smile. It was that same smile that carried him through his painful illness, preserving his humanity intact to the very end. My wife and I grieve for him and shall always cherish his memory in our hearts.
Stamatis is survived by his wife Miranda and his two sons, Alexis, a second year medical student at the University of Pennsylvania, and Thanassis, a sophomore at the University of North Carolina.
Elias Masry
University of California,
San Diego, May 10, 1995