Ron Getoor

Ronald Kay Getoor, Professor Emeritus in the Department of Mathematics at the University of California, San Diego, died peacefully at his home on October 28, 2017. He was 88.

Getoor was born in Royal Oak, Michigan, on February 9, 1929. He attended the University of Michigan, receiving an A.B. in Mathematics in 1950, an M.S. in Mathematics in 1951, and a PhD in Mathematics in 1954 under the direction of Arthur H. Copeland. Getoor spent two post-doctoral years (1954–1956) at Princeton University as a Fine Instructor. At Princeton, he came in contact with William Feller, Kiyoshi Itô, and Henry P. McKean, Jr. (then Feller’s student). Itô had a profound impact on Getoor, influencing the direction of his research in the years that followed. Getoor was appointed Assistant Professor at the University of Washington in 1956, arriving in the same year as his future collaborator Robert M. Blumenthal. Getoor had advanced to Full Professor by the time he moved south to the nascent Mathematics Department at UC San Diego in 1966. He spent the rest of his career at UC San Diego, achieving the highly distinguished rank of Professor Above-Scale. Although he formally retired in 2000, he continued an active research program until about 2010. Getoor visited various other institutions over the years, including MIT in 1959-60 under an NSF postdoctoral fellowship and Stanford University on a sabbatical.

Getoor was one of the leaders in the growth of Probability Theory that began in the 1950s and continues to this day. His research career spanned more than 50 years, and during that time he focused on the study of stochastic processes, principally Markov processes. In the late 1950s, Getoor and Blumenthal set out to understand the then-recent work of Gilbert Hunt on the connection between Markov processes and potential theory (extending the connections between Brownian motion and Newtonian potential theory that were known to Perron, Wiener, Kakutani, and others). They succeeded in this mission, and developed a detailed theory of the “additive functionals” of such Markov processes, resulting in the foundational work Markov Processes and Potential Theory, which appeared in 1968. Offshoots of this program were illuminating and groundbreaking work on stable processes and on the local times of Markov processes. This work has had a lasting impact on the field, and is frequently cited even today.

Shortly after moving to San Diego, Getoor started a second long-term collaboration with Michael J. Sharpe, who joined the UC San Diego mathematics faculty in 1967. Their joint work covered an impressive stretch, from abstract results on general Markov processes to detailed investigation of the intricate behavior of Bessel processes. Perhaps the most important of this work was the influential paper “Conformal Martingales” and their extensive work on last-exit times and excursions.

Starting in the early 1980s, Getoor became interested in the so-called Kuznetsov process, which is the stationary version of a given strong Markov process, with time extending to infinity in both directions. Such a process provides a probabilistic embodiment of the analytic duality relationship that was a cornerstone of the earlier work with Blumenthal. This path-wise view of “time reversal” became a key tool in the detailed study of the excessive measures of a Markov process. These studies, some in collaboration with Patrick J. Fitzsimmons, culminated in Getoor’s definitive monograph on the subject Excessive Measures, which appeared in 1990.

Over his career, Getoor published more that 100 research articles and three books. Two of these books have been mentioned above; the third is the brief Markov processes: Ray processes and right processes (1975), which describes with admirable lucidity how the “Ray-Knight compactification” can be used in the study of strong Markov processes. Getoor’s papers are notable for their clarity of exposition and attention to detail.

Getoor was elected a Fellow of the IMS in 1971, and was among the inaugural class of Fellows of the American Mathematical Society, in 2013. He was an invited speaker at the 1970 International Congress of Mathematicians (ICM) in Nice.

Getoor was a dedicated teacher and mentor. Over the years he taught mathematics courses at all levels. He supervised the Ph.D. theses of nine students at UC San Diego, and he hosted post-doctoral visits to UC San Diego of several other mathematicians. Along with Kai Lai Chung and Erhan Çinlar, he founded in 1981 the “Seminar on Stochastic Processes,” a yearly gathering of “kindred spirits working on stochastic processes” with the aim of stimulating discussion and collaboration. The “Seminar” has continued uninterrupted for more than 35 years.

As one of the senior members of the mathematics department, Getoor helped shape the growth of the department and especially of the probability group, as UC San Diego grew over the years. He was known within the department and around campus for his sage advice and was tapped to serve on the all important Academic Senate Committee on Academic Personnel (then called the Budget Committee). Once the faculty club was built in 1988, Getoor enjoyed lunching at Euclid’s table with mathematics colleagues and mathematics buffs from around campus; he also helped advise the club by serving on its Board of Directors.

As a young man Getoor was a competitive table tennis player and won a state championship. Throughout his life, Getoor enjoyed the outdoors, including hiking, body surfing (particularly at Scripps, Torrey Pines and Del Mar), and he enjoyed road trips to wine country, the California and Pacific Northwest coasts, and national parks. He was an avid fan of classical music and the opera, attending the San Diego Opera as a season subscriber for many years.

Ron is survived by his second wife Anne Westbrook Getoor, his daughter Lise Getoor who is a professor in the Computer Science department at UC Santa Cruz, his brother Richard Getoor of Cincinnati, OH, his sister Jackie Kuthy of Fort Lauderdale, FL, stepchildren Thomas Westbrook and John Westbrook, step grandchildren Emma, Lilli, Marian, and Philip, and nieces and nephews including Donna Beshgetoor of San Diego.

Those wishing to honor Ron Getoor’s memory are asked to donate to the Ronald Getoor Memorial Fund for Mathematical Probability Research at UC San Diego. Donations can be made online at http://bit.ly/GetoorMemorialFund. A memorial gathering will be scheduled at a later date for family, friends and colleagues.

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Written by Patrick J. Fitzsimmons, Michael J. Sharpe and Ruth J. Williams,
University of California, San Diego