Lester Dubins

Lester Dubins (April 27, 1920 – February 11, 2010) was an American mathematician noted primarily for his research in

His doctoral students include Theodore Hill. Together with Gideon E. Schwarz he proved the Dubins–Schwarz theorem.

Publications

• Dubins–Spanier theorems
• Dubins, L. E. (1957). "On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents". American Journal of Mathematics. 79 (3): 497–516.
  JSTOR 2372560
  .
• Dubins, Lester E. (1957). "Conditional Probability Distributions in the Wide Sense".
  JSTOR 2032685
  .
• Dubins, Lester E. (1960). "Another Proof of the Four Vertex Theorem". The American Mathematical Monthly. 67 (6): 573–574.
  JSTOR 2309181
  .
• Dubins, Lester E. (1960). "On Differentiation of Series Term-By-Term". The American Mathematical Monthly. 67 (8): 771–772.
  JSTOR 2308657
  .
• Dubins, Lester E.; Savage, Leonard J. (1960). "Optimal Gambling Systems". Proceedings of the National Academy of Sciences of the United States of America. 46 (12): 1597–1598.
  PMID 16590787
  .
• Dubins, Lester E.; Morgenthaler, George W. (1961). "Inclusion of Detection in Probability of Survival Models". Operations Research. 9 (6): 782–801.
  JSTOR 167046
  .
• Blackwell, David; Dubins, Lester E. (1963). "Sharp Bounds on the Distribution of the Hardy-Littlewood Maximal Function".
  JSTOR 2033819
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• Dubins, Lester E.; Freedman, David A. (1965). "A Sharper Form of the Borel-Cantelli Lemma and the Strong Law". The Annals of Mathematical Statistics. 36 (3): 800–807.
  JSTOR 2238191
  .
• Dubins, Lester E.; Savage, Leonard J. (1965). "A Tchebycheff-Like Inequality for Stochastic Processes". Proceedings of the National Academy of Sciences of the United States of America. 53 (2): 274–275.
  PMID 16591259
  .
• Dubins, Lester E.; Schwarz, Gideon (1965). "On Continuous Martingales". Proceedings of the National Academy of Sciences of the United States of America. 53 (5): 913–916.
  PMID 16591279
  .
• Dubins, Lester E. (1966). "A Note on Upcrossings of Semimartingales". The Annals of Mathematical Statistics. 37 (3): 728.
  JSTOR 2238744
  .
• Dubins, Lester E.; Freedman, David A. (1966). "Invariant Probabilities for Certain Markov Processes". The Annals of Mathematical Statistics. 37 (4): 837–848.
  JSTOR 2238573
  .
• Dubins, Lester E.; Freedman, David A. (1966). "On the Expected Value of a Stopped Martingale". The Annals of Mathematical Statistics. 37 (6): 1505–1509.
  JSTOR 2238767
  .
• Dubins, Lester E.; Teicher, Henry (1967). "Optimal Stopping When the Future is Discounted". The Annals of Mathematical Statistics. 38 (2): 601–605.
  JSTOR 2239174
  .
• Dubins, Lester E. (1968). "A Simpler Proof of Smith's Roulette Theorem". The Annals of Mathematical Statistics. 39 (2): 390–393.
  JSTOR 2239033
  .
• Dubins, Lester E. (1968). "On a Theorem of Skorohod". The Annals of Mathematical Statistics. 39 (6): 2094–2097.
  JSTOR 2239305
  .
• Dubins, Lester E. (1972). "Sharp Bounds for the Total Variance of Uniformly Bounded Semimartingales". The Annals of Mathematical Statistics. 43 (5): 1559–1565.
  JSTOR 2240078
  .
• Dubins, Lester E. (1973). "Which Functions of Stopping Times are Stopping Times?". The Annals of Probability. 1 (2): 313–316.
  JSTOR 2959492
  .
• Dubins, Lester E. (1974). "On Lebesgue-like Extensions of Finitely Additive Measures". The Annals of Probability. 2 (3): 456–463.
  JSTOR 2959178
  .
• Dubins, Lester E.; Meilijson, Isaac (1974). "On Stability for Optimization Problems". The Annals of Probability. 2 (2): 243–255.
  JSTOR 2959222
  .
• Blackwell, David; Dubins, Lester E. (1975). "On Existence and Non-Existence of Proper, Regular, Conditional Distributions". The Annals of Probability. 3 (5): 741–752.
  JSTOR 2959116
  .
• Dubins, Lester E. (1975). "Finitely Additive Conditional Probabilities, Conglomerability and Disintegrations". The Annals of Probability. 3 (1): 89–99.
  JSTOR 2959267
  .
• Dubins, Lester E.; Sudderth, William D. (1975). "An Example in which Stationary Strategies are not Adequate". The Annals of Probability. 3 (4): 722–725.
  JSTOR 2959335
  .
• Dubins, Lester E. (1977). "Group Decision Devices". The American Mathematical Monthly. 84 (5): 350–356.
  JSTOR 2319963
  .
• Dubins, Lester E. (1977). "Measurable, Tail Disintegrations of the Haar Integral are Purely Finitely Additive".
  JSTOR 2041941
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• Dubins, Lester E. (1977). "On Everywhere-Defined Integrals". Transactions of the American Mathematical Society. 232: 187–194.
  JSTOR 1998933
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• Dubins, Lester E.; Sudderth, William D. (1977). "Persistently ϵ-Optimal Strategies".
  JSTOR 3689649
  .
• Dubins, Lester E.; Gilat, David (1978). "On the Distribution of Maxima of Martingale".
  JSTOR 2043117
  .
• Dubins, Lester E.; Pitman, Jim (1979). "A Pointwise Ergodic Theorem for the Group of Rational Rotations". Transactions of the American Mathematical Society. 251: 299–308.
  JSTOR 1998695
  .
• Dubins, Lester E.; Sudderth, William D. (1979). "On Stationary Strategies for Absolutely Continuous Houses". The Annals of Probability. 7 (3): 461–476.
  JSTOR 2243199
  .
• Dubins, Lester E.; Pitman, Jim (1980). "A Divergent, Two-Parameter, Bounded Martingale".
  JSTOR 2042335
  .
• Dubins, Lester E. (1982). "A Zero-One, Borel Probability which Admits of No Countably Additive Extensions".
  JSTOR 2043394
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• Blackwell, David; Dubins, Lester E. (1983). "An Extension of Skorohod's Almost Sure Representation Theorem".
  JSTOR 2044607
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• Dubins, Lester E. (1983). "A Gloss on a Theorem of Furstenberg".
  JSTOR 2045487
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• Dubins, Lester E.; Heath, David (1983). "With Respect to Tail Sigma Fields, Standard Measures Possess Measurable Disintegrations".
  JSTOR 2044985
  .
• Dubins, Lester E.; Heath, David (1984). "On Means with Countably Additive Continuities".
  JSTOR 2044640
  .
• Dubins, Lester E. (1996). "The Gambler's Ruin Problem for Periodic Walks". Lecture Notes-Monograph Series. Institute of Mathematical Statistics Lecture Notes - Monograph Series. 30: 7–12.
  JSTOR 4355934
  .
• Dubins, Lester E.; Gilat, David; Meilijson, Isaac (2009). "On the Expected Diameter of an L₂-Bounded Martingale". The Annals of Probability. 37 (1): 393–402.
  S2CID 115157104
  .
• Dubins, Lester E.; Savage, Leonard J. (1965). How to gamble if you must: inequalities for stochastic processes. McGraw–Hill series in probability and statistics. McGraw–Hill.