mathematics

Ronald Getoor

Ronald Getoor is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Ronald Getoor rather than just read about it. In short: Ronald Kay Getoor (9 February 1929, Royal Oak, Michigan – 28 October 2017, La Jolla, San Diego, California) was an American mathematician. Getoor received from the University of Michigan bachelor's degree in 1950, master's degree in 1951, and Ph.D. in 1954 under Arthur Herbert Copeland with thesis Connections between operators in Hilbert space and random functions of second order.

Key takeaways

Ronald Getoor belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Ronald Getoor to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Ronald Getoor from memory before moving on to harder problems.

Reference excerpt

Ronald Kay Getoor (9 February 1929, Royal Oak, Michigan – 28 October 2017, La Jolla, San Diego, California) was an American mathematician. Getoor received from the University of Michigan bachelor's degree in 1950, master's degree in 1951, and Ph.D. in 1954 under Arthur Herbert Copeland with thesis Connections between operators in Hilbert space and random functions of second order. As a postdoc he was an instructor at Princeton University. He became in 1956 an assistant professor and then full professor at the University of Washington. During the academic year 1964–1965 he was a visiting professor at Stanford University. From 1966 until his retirement in 2000 he was a professor at the University of California, San Diego. Getoor's research deals with probability theory, especially the theory of Markov processes and potential theory. In 1970 he was an invited speaker at the International Congress of Mathematicians in Nice. He was elected a Fellow of the Institute of Mathematical Statistics and in 2012 a Fellow of the American Mathematical Society.

Scientific work In the late 1950s, Getoor and Robert Blumenthal set out to understand the work of Gilbert Hunt on the connection between Markov processes and potential theory, extending the connections between Brownian motion and Newtonian potential theory. Getoor's 1968 book Markov Processes and Potential Theory, co-authored with Blumenthal, became a reference on the topic. Together with Blumenthal and Sharpe, Getoor obtained many results on the fine structure of Markov processes and martingales, in particular the theory of local time for Markov processes. With Michael J. Sharpe, Getoor defined the notion of 'conformal martingale', which proved to be influential in potential theory, investigated the behavior of Bessel processes, last-exit times and excursions. Starting in the early 1980s, Getoor studied stationary extensions of a given strong Markov process, with time extending to infinity in both directions, formulating a pathwise view of "time reversal" which became a key tool in his studies of the excessive measures of a Markov process. The 'Blumenthal-Getoor index', a concept which characterises the nature of discontinuities of Lévy processes and semi-martingales, is named after him.

Personal life He married in 1959. His wife Ann Getoor worked on the design of commercial aircraft at Boeing, and his daughter Lise Getoor is a professor of computer science at the University of California, Santa Cruz. Getoor died at home on October 28, 2017, in La Jolla at the age of 88.

Selected publications Books Markov processes: Ray processes and right processes. Lecture Notes in Mathematics 440. Springer Verlag. 1975. Getoor, R. K. (15 November 2006). 2006 reprint. Springer. ISBN 9783540374220; pbk, 124 pages{{cite book}}: CS1 maint: postscript (link) with Robert McCallum Blumenthal: Markov Processes and Potential Theory. Academic Press. 1968. Excessive Measures. Birkhäuser. 1990. Getoor, R. K. (6 December 2012). 2012 reprint. Springer. ISBN 9781461234708; pbk, 190 pages{{cite book}}: CS1 maint: postscript (link) Articles Blumenthal, R. M.; Getoor, R. K. (1960). "Some theorems on stable processes". Trans. Amer. Math. Soc. 95 (2): 263–273. doi:10.1090/S0002-9947-1960-0119247-6. Blumenthal, R. M.; Getoor, R. K. (1961). "Sample functions of stochastic processes with stationary independent increments". Journal of Mathematics and Mechanics. 10 (3): 493–516. JSTOR 24900735. Blumenthal, R. M.; Getoor, R. K.; Ray, D. B. (1961). "On the distribution of first hits for the symmetric stable processes". Trans. Amer. Math. Soc. 99 (3): 540–554. doi:10.1090/S0002-9947-1961-0126885-4. Blumenthal, R. M.; Getoor, R. K. (1964). "Additive functionals of Markov processes in duality". Trans. Amer. Math. Soc. 112: 131–163. doi:10.1090/S0002-9947-1964-0160269-0. Blumenthal, R. M.; Getoor, R. K. (1964). "Local times for Markov processes". Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete. 3 (1): 50–74. doi:10.1007/BF00531683. S2CID 120071327. Getoor, R. K.; Sharpe, M. J. (1972). "Conformal martingales". Inventiones Mathematicae. 16 (4): 271–308. Bibcode:1972InMat..16..271G. doi:10.1007/BF01425714. S2CID 189830360.

References

External links Getoor, Ronald K., Royal Oak High School Hall of Fame Complete bibliography

Illustrations

Worked examples

Example 1 — a first encounter with Ronald Getoor

Start with the simplest possible case. Write down what Ronald Getoor claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Ronald Getoor before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Ronald Getoor ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Ronald Getoor

In research: Ronald Getoor appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Ronald Getoor in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Ronald Getoor is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1929 births, 2017 deaths, American probability theorists, so understanding it makes those chapters shorter.
In everyday life: Look for Ronald Getoor outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Ronald Getoor in 20 minutes

Read the reference excerpt below once, without taking notes.
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Frequently asked questions

What is Ronald Getoor in simple terms?

Why does Ronald Getoor matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Ronald Getoor?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Ronald Getoor.