Probability: A Survey of the Mathematical Theory (New York: W.A. Benjamin, 1966). This short book on the classical core of probability theory was the result of a course I gave at Dartmouth College around 1965. The book was well received in the U.S., and when I visited Moscow in 1970 I met a young mathematician who was translating it and preparing a Russian edition. The result appeared in 1973 as a paperback, published by "Nauka" ("Science") of Moscow. They printed 68,000 copies and sold them for 33 kopeks!
Stochastic Processes: A Survey of the Mathematical Theory (New York: Springer Verlag, 1977). This book is Volume 23 in "Applied Mathematical Sciences." It began as notes for an all-year course of lectures I gave in Aarhus University (Denmark) in 1972-73, and was first published as an Aarhus lecture notes volume. This book also had an edition in Russian, published in Kiev in 1983. The edition was only 2000 copies this time (a reasonable number) and the price was 1.80 rubles.
Probability: A Survey of the Mathematical Theory, second edition (New York: John Wiley & Sons, 1996). In preparing the new edition I tried to make the book more user-friendly with clearer examples, more problems, and some better explanations, while keeping the brevity and (I hope) other virtues of the original. The subjects covered are roughly the same as in the first edition.
Research articles (mathematics)
I have published around 40 mathematical articles, some of which I think had value in their field or at least in my mathematical development. I'll list here a few of the more significant ones with a brief commentary.
3. "On the coefficients of reciprocal power series," Amer. Math. Monthly vol. LXV (1958), pp. 433-448. This one is significant for me because it was the first real paper I wrote (although not the first to appear). It's cute although not very important--uses Markov chain ideas to get some results on formal power series.
4. "Some limit theorems for stochastic processes," Journal of Math. and Mechanics vol. 7 (May 1958). Important to me because it was the main part of my Cal. Tech. PhD thesis. Through good fortune my advisor was Frank Spitzer, who was then a little-known assistant professor but who would soon be recognized as an original and creative probabilist.
5. "An occupation time theorem for certain stochastic processes," Trans. Amer. Math. Soc. vol. 88 (1960), pp. 380-387. This was the other part of my thesis.
7. "On the isometries of certain function spaces," Pacific Journal of Math. vol. 8 (1958), pp. 445-466. The main point here was to give a nice derivation of the isometries of Lp spaces when p is not 2. There were some fringe benefits too. This paper has been cited more than any other of mine which is not about probability.
13. "Criteria for the recurrence or transience of stochantic processes," Journal of Math. Analysis and Applications vol. 1 (1960), pp. 314-330. This paper was the start of a series with a common idea. I was fascinated by the behaviour of simple random walks (coin tossing process), and I thought that if the probabilities for that coin were just a little different from 1/2, 1/2, the difference going to 0 when the walk was far away from the origin, then the long run behaviour wouldn't change. For example, how different must the transition probabilities be in order to change the process from recurrent to transient? I found that adding c/n to the transition probability pn,n+1 was the critical factor, and the behaviour then depends on the value of that constant c. To generalize the example, martingale methods were an excellent tool.
16. "A new class of probability limit theorems," Journal of Math. and Mech. vol. 11 (1962), pp. 749-772.
18. "Semi-stable stochastic processes," Trans. Amer. Math. Soc. vol. 104 (1962), pp. 62-78. This paper defined and discussed the class of processes which can appear as the asymptote of some other process when the time and space scales are expanded appropriately. The leading example is the Brownian motion process, which is obtained as the limit of (for example) a simple random walk after changes of scale. Other examples are given by the limit theorems in papers #16 and #26. I chose the name "semi-stable" for these limiting processes because of their analogy with stable process as the limits for scaled sums of independent random variables. Later others coined the term "self-similar" for the same class of processes, and I must admit that it is a better and more descriptive name. Both terms have been used by other authors.
23. "Criteria for stochastic processes II: passage time moments," Journal of Math. Analysis and Applications vol. 7 (1963), pp. 127-145. This paper was a sequel to #13, using very similar methods.
26. "On extreme order statistics," Annals of Math. Statistics vol. 35 (1964), pp. 1726-1737.
29. "Limit distributions for branching processes," Proc. of the 5th Berkeley Symp. on Probability and Statistics vol. ii, pp. 225-241 (Univ. of California Press, 1967).
30. "Conditional limit theorems for branching processes" (with Peter Ney), Theory of Probability and Its Applications (Russian), vol. 13 (1968), pp. 126-137. This paper earned me an "Erdos number" of 2, since Peter was an Erdos coauthor at some point.
32. "The limit of a sequence of branching processes," Zeitschrift fur Wahrscheinlickkeits- theorie vol. 7 (1967), pp. 271-288.
33. "Continuous-state branching processes," Bull. Amer. Math. Soc. vol 73 (1967), no. 3, pp. 382-386. This "research announcement" described a construction of such processes from certain Levy processes using a random time change. I stated the theorem and promised that the proof would appear elsewhere, but I never published it. Fortunately the promise has been fulfilled by others.
39. "Semi-stable Markov processes I," Zeitschrift fur Wahrscheinlickkeitstheorie vol. 22 (1972), pp. 205-225. This article gives a construction for semi-stable Markov processes on the positive real axis, showing that by means of a random time change and a logarithmic transformation of the state space each such process can be reduced to a process with stationary independent increments (Levy process).
41. "Remarks on maximal branching processes," Theory of prob. and applications (Moscow) vol. 17 (1972), pp. 46-54. This paper was a "souvenier" of my 1970 visit to Moscow, and includes a (very short) abstract in Russian. The results are not important, but there is one beautiful little curiosity. My criterion for the recurrence of these processes involves in one formula three "magic numbers" of mathematics: pi, e, and Euler's constant c. I didn't try to put them in there, that's just how it came out!
Book Review: Amer. Math. Monthly, October 1974. The book in question was Mathematics in Society. Elements of an Analysis: History, Education, Ideology (in Danish), by Elsa and Jens Høyrup. I encountered this book and became acquainted with the authors while visiting Denmark in 1972-73. I was enough impressed with their work to later prepare an English translation of the book. I could not find an American publisher for Math in Society but the translation had some influence through circulation in "samizdat."
BOOKS (social issues and policy)
The Nuclear Almanac: Confronting the Atom in War and Peace (Reading, MA: Addison-Wesley, 1984). I contributed 3 chapters to this multi-author book which was "compiled and edited by faculty members at M.I.T." The authors' hope was to bring greater reason to bear on what was then (as now) a very frightening area of U.S. policy. My involvement came as a result of working with the NARMIC project of the American Friends Service Committee in 1980.
What Are We Afraid Of? An Assessment of the "Communist Threat" in Central America (Boston: South End Press, 1988). This short book, a critique of U.S. policy, was also a spin-off from working with NARMIC, this time following my first trip to Central America in 1985. The concept for what was originally a NARMIC pamphlet and then a book was to counter the "Red Scare" tactics the Reagan administration was using to justify sponsoring war and repression in the region.
Enrique Alvarez Córdova: Life of a Salvadoran Revolutionary and Gentleman (Jefferson, NC: McFarland, 2006). For a biographical sketch of Enrique Alvarez see the "Central America" section of this web site. I wanted to write Enrique's story since around 1986, when I first heard of the Salvadoran oligarch who became a leader of the revolution. I decided then that the project had to wait until the end of the Salvadoran civil war, and until I could speak some Spanish. I worked on the book off and on for about 10 years, and made about that many trips to El Salvador in the process.
Articles, etc. (social issues and policy)
Acceptable Risk? The Nuclear Age in the United States was a 30 minute slidefilm which I co-wrote and co-produced with David Goodman for the AFSC's NARMIC project in 1980. I was also co-author of the booklet Documentation: Background and explanation to accompany 'Acceptable Risk?' published by AFSC that same year.
"Crisis Relocation Planning: What harm can it do?," Bulletin of the Atomic Scientists vol. 39, no. 6 (1983), pp. 7s-10s.
"What Are We Afraid Of? Facts and Fears About the 'Communist Threat' in Central America" is a 16-page pamphlet in question-and-answer format published in December 1986 by the American Friends Service Committee. This was the origin of my book on Central America policy which amplifies the themes found here.
"Costa Rica: Democracy Under Siege" was another AFSC pamphlet, this one of 32 pages published in December 1989. The subtitle "The Impact of U.S. Intervention" describes the main theme of the paper, which also includes a historical sketch.
"The King of Denmark and the Yellow Star," Non-Violent Activist, May-June 2002.
"Historias of El Salvador" are found in the Central America pages of this site. I am especially intrigued by the "Justo Armas" mystery and hope to do more about this in the near future. Please write me if you can contribute anything to its solution!
"Florida 2006: Can Statistics Tell Us Who Won Congressional District-13?" (with Arlene Ash), Chance vol. 21, no. 2 (2008), pp. 18-24.
"Elections 2012: Suppressing Fraud or Suppressing the Vote?" (with Arlene Ash), Statistics, Politics and Policy vol. 4, no. 1, pp. 14-28, January 2013.
Well, that's a start. I contributed quite a few articles to the old WIN magazine of the War Resisters League, on themes such as nonviolence, Denmark's "free city" Christiania, politics, nuclear power, and more. I wrote for other now-defunct publications, including the Vermont Freeman, an alternative paper that no longer exists. There are also a good many pieces in Peacework, the magazine of the AFSC's New England office; it too (alas) is no longer published due to the organization's financial problems. I've had one article in each of several other magazines, including The Progressive, In These Times, and Fellowship. The Chance article on voting was mentioned on the opening page. Since 2008 I have also contributed quite a few essays and "op-ed" style commentaries to the web magazine TruthOut. I expect there will be additions to this list, so stay tuned.