476:: Doob kept a card file of ideas for theses. When he got a new graduate student he would pull out a card and suggest the problem on the card. If the student could not solve it, Doob put it back in the file and chose the next card...I succeeded on the third card, which proposed extending to submartingales an inequality called the "upcrossing inequality" that Doob proved for martingales and used to prove his
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102:(1957) which described probability theory, linear algebra, and applications in sociology, genetics, psychology, anthropology, and economics. They found "the basic ideas of finite mathematics were easier to state and theorems about them considerably easier to prove than their infinite counterparts." A French translation was made by M. C. Loyau and published in 1960 by Donod.
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of any of the random variables, given the previous outcomes, is equal to the last outcome. Thus, if we interpret the outcomes as our fortune in a game, at each stage the game seems fair. So, we can think of a martingale as representing a fair game. If the expected value is less than or equal to the
134:
with Kemeny. As the "first self-contained account in
English", it attracted wide interest. While one reviewer said "the exposition is of high quality", other reviewers found fault: Too little attention paid to assumptions inherent in a model. "Interest builds steadily as one peruses the book." But
117:
which included applications: computer circuits, critical path analysis, flow diagrams for computing and accounting procedures, Monte Carlo simulation of decision processes, reliability, decision theory, waiting line theory, a simple approach to mathematics of finance, matrix games, and the simplex
452:
last outcome, then we say the process is a supermartingale and, if it is greater than or equal to the last value, then it is called a submartingale. Thus, a supermartingale represents an unfavorable game and a submartingale a favorable game. These names are suggested by probabilistic
135:"little attention to historical development." "From the point of view of an undergraduate ... the opening chapter on mathematical prerequisites is rather frightening." "Does not supersede the corresponding chapters in Feller's classic
78:. Doob assigned such topics by having students attempt to solve a series of problems that he kept on file cards. Snell earned his Ph.D. in 1951 ("Applications of Martingale System Theorems"), with Doob as his supervisor.
50:, an adventure author, and Lucille, a concert pianist. Lucille taught the three sons (Jud, John and Laurie) to play piano, cello, and violin. The family had a life-lease on a cabin in
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109:(1959) for sophomores at Dartmouth studying science. Infinite problems are considered after their finite counterparts are fully developed in the text. In 1962 the publisher
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Snell became involved in a mathematics department project to develop a course on modern mathematics used in biological and social sciences. He worked with
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in 1992 to "review news and journal articles pertaining to probability and statistics in the real world." One feature is
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in the
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method for solving linear programming problems. A second edition of the first text came out in 1966.
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1980: (with Ross P. Kindermann) "On the relation between Markov random fields and social networks",
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issued a third book from a
Dartmouth team: Kemeny, Snell, Thompson, and Arthur Schleifer Jr. wrote
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with positive probability, which implies that the submartingale converges with probability 1.
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for statistical gaffes in media reports, a column originally found in the newsletter of the
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dominating the price process. The Snell envelope refers to results in a 1952 paper
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Another colleague at
Dartmouth, Hazleton Mirkil, joined the team to write
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for the expected number of times the sample path can go from below
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654:, then the sample paths cannot oscillate infinitely often between
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J. L. Snell (1952) "Applications of martingale system theorems",
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J.L. Snell (1959) "Finite Markov Chains and Their
Applications",
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19:
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with
Charles M. Grinstead and William P. Peterson, a book
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1962: (with Kemeny, Thompson & Arthur
Schleifer Jr.)
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Snell retired in 1995 and was elected as a fellow of the
139:; "No index and not even the sketchiest bibliography."
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546:
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1959: (with Kemeny, Thompson & Hazleton Mirkil)
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850:Transactions of the American Mathematical Society
822:Proceedings of the Edinburgh Mathematical Society
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409:2011: (with C.M. Grinstead & W.P. Peterson)
940:Fellows of the American Statistical Association
789:Journal of the American Statistical Association
379:second edition, American Mathematical Society,
70:from 1948 through 1951; Doob introduced him to
702:J.L. Snell (2005) "Obituary: Joseph L. Doob",
474:Quoted from Snell's Obituary of Joseph L. Doob
443:: A discrete-time martingale is a sequence of
441:Quoted from Snell's Obituary of Joseph L. Doob
38:) was an American mathematician and educator.
288:Finite Mathematics with Business Applications
115:Finite Mathematics with Business Applications
126:In 1959 Snell published a survey article on
311:Markov Random Fields and Their Applications
302:1966: (with J.G. Kemeny & A.W. Knapp)
294:Mathematical Models in the Social Sciences
235:Applications of martingale system theorems
54:where they would go for summer holidays.
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866:Literature by and about J. Laurie Snell
194:models, estimating expected value of a
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480:. This inequality for a submartingale
447:with finite expectation such that the
306:, second edition 1976, Springer-Verlag
724:Algèbre Moderne et Activités Humaines
130:. He worked the material into a book
910:21st-century American mathematicians
905:20th-century American mathematicians
343:Random Walks and Electrical Networks
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347:Mathematical Association of America
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540:, give an upper bound in terms of
456:, where martingales correspond to
256:Introduction to Finite Mathematics
100:Introduction to Finite Mathematics
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687:Michigan Technological University
336:Journal of Mathematical Sociology
62:Snell studied mathematics at the
212:American Statistical Association
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643:{\displaystyle E(|Y_{n}|)<k}
525:{\displaystyle Y_{1},Y_{2},...}
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704:Journal of Applied Probability
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268:Finite Mathematical Structures
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30:(January 15, 1925 in Wheaton,
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935:University of Illinois alumni
885:Mathematics Genealogy Project
809:American Mathematical Monthly
753:American Journal of Sociology
737:American Mathematical Monthly
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598:. This bound implied that if
415:American Mathematical Society
315:American Mathematical Society
309:1980: (with Ross Kindermann)
180:American Mathematical Society
162:where there is an archive of
34:– March 19, 2011 in Hanover,
945:Mathematicians from Illinois
876:Website at Dartmouth College
341:1984: (with Peter G. Doyle)
292:1962: (with John G. Kemeny)
272:1960: (with John G. Kemeny)
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766:Quarterly Review of Biology
377:Introduction to Probability
360:Introduction To Probability
198:ticket, and reliability of
170:. Out of collaborations in
137:Introduction to Probability
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579:{\displaystyle E(|Y_{n}|)}
276:, D. van Nostrand Company
950:American textbook writers
712:10.1017/S002190020000019X
304:Denumerable Markov Chains
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152:Royal Statistical Society
52:Isle Royale National Park
930:Dartmouth College alumni
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178:(2011) was published by
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838:Information and Control
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650:for some constant
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402:2011-07-27 at the
252:Gerald L. Thompson
229:, is the smallest
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76:probability theory
28:James Laurie Snell
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23:James Laurie Snell
834:Benoit Mandelbrot
422:978-0-8218-5261-3
411:Probability Tales
393:978-0-8218-0749-1
330:978-0-8218-5001-5
176:Probability Tales
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920:2011 deaths
915:1925 births
852:73: 293–312
532:would, for
338:7(1): 1–13.
223:stochastics
200:fingerprint
172:Chance News
160:Chance Wiki
156:Chance News
144:Chance News
72:martingales
894:Categories
791:56: 182,3
755:66(1): 427
739:66: 99–104
670:References
221:, used in
154:. In 2005
872:catalogue
590:to above
214:in 1996.
164:Forsooths
98:to write
48:Roy Snell
42:Biography
400:Archived
148:Forsooth
122:Writings
32:Illinois
883:at the
868:in the
836:(1960)
787:(1961)
751:(1961)
196:lottery
768:37(1)
420:
397:online
391:
383:
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358:1988:
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262:Online
206:Legacy
186:(like
824:12(1)
536:<
428:Notes
241:Books
66:with
658:and
635:<
418:ISBN
389:ISBN
381:ISBN
367:ISBN
350:ISBN
326:ISBN
318:ISBN
278:ISBN
250:and
225:and
217:The
168:News
94:and
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708:doi
86:At
896::
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