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Dr. David Blackwell's Publications

  1. "Idempotent Markoff chains," Ann. of Math., Vol. 43, No. 3 (1942), pp. 560-567.
  2. "The existence of anormal chains," Bull. Amer. Math. Soc., Vol. 51 (1945) pp. 465-468.
  3. "Finite non-homogeneous chains," Ann. of Math., Vol. 46, No. 4 (1945), pp. 594-599.
  4. "On an equation of Wald," Ann. Math. Stat., Vol. 17, No. 1 (1946), pp. 84-87
  5. 5. "On functions of sequences of independent chance vectors with applications to the problem of the `random walk' in k dimensions," Ann. Math. Stat., Vol. 17, No. 3 (1946), pp. 310-317 (with M.A. Girshick).
  6. "Conditional expectation and unbiased sequential estimation," Ann. Math. Stat., Vol. 18, No. 1 (1947), pp. 105-110.
  7. "A lower bound for the variance of some unbiased sequential estimates," Ann. Math. Stat., Vol. 18, No. 2 (1947), pp. 277-280. (with M.A. Girshick).
  8. "A renewal theorem," Duke Math. Jour., Vol. 15, No. 1 (1948), pp. 145-150.
  9. "Bayes and minimax solutions of sequential decision problems," Econometrica, Vol. 17, Nos. 3 and 4 (1949), pp. 213-244 (with K.J. Arrow and M.A. Girshick).
  10. "Some two-person games involving bluffing," Proc. Nat. Acad.Sci., Vol. 35, No. 10 (1949), pp. 600-605, (with R. Bellman).
  11. "Comparison of experiments," Proc. Second Berkeley Symposium on Math. Stat. and Prob., University of California Press, 1951.
  12. "The range of certain vector integrals," Proc. Am. Math. Soc., Vol. 2, No. 3 (1951), pp. 390-395.
  13. "On a theorem of Lyapunov," Ann. Math. Stat., Vol. 22, No. 1, (1951), pp. 112-114.
  14. "On moment spaces," Ann. of Math., Vol. 54, No. 2 (1951), pp. 272-274. (with R. Bellman).
  15. "On the translation parameter problem for discrete variables," Ann. Math. Stat., Vol. 22, No. 3 (1951), pp. 393-399.
  16. "Admissible points of convex sets," Contributions to the Theory of Games, Vol. 2, Princeton University Press, 1953, pp. 87-91 (with K.J. Arrow and E.W. Barankin).
  17. "On randomization in statistical games with k terminal action," Contributions to the Theory of Games, Vol. 2, Princeton University Press, 1953, pp. 183-187.
  18. "Extension of a renewal theorem," Pacific Jour. of Math., Vol. 3, No. 2 (1953), pp. 315-320.
  19. "Equivalent comparisons of experiments," Ann. Math. Stat., Vol. 24, No. 2 (1953), pp. 265-272.
  20. "On optimal systems," Ann. Math. Stat., Vol. 25, No. 2 (1954), pp. 394-397.
  21. "A representation problem," Proc. Amer. Math. Soc., Vol. 5, No. 2 (1954), pp. 283-287.
  22. Theory of Games and Statistical Decisions, Wiley and Sons, 1954, xi+355 pp. (with M.A. Girshick).
  23. "On multi-component attrition games," Naval Research Logistics Quarterly, Vol. 1 (1954), pp. 210-216.
  24. "On transient Markov processes with a countable number of states and stationary transition probabilities," Ann. Math. Stat., Vol. 26, No. 4 (1955), pp. 654-658.
  25. "An analog of the minimax theorem for vector payoffs," Pacific Jour. of Math., Vol. 6, No. 1 (1956), pp. 1-8.
  26. "On a class of probablity spaces," Proc. Third Berkeley Symposium on Math. Stat. and Prob., University of California Press, Vol. 2 (1956), pp. 1-6.
  27. "Controlled random walks," Proc. of the Internat. Congress of Mathematicians, Amsterdam 1954; Vol. 3 (1956), pp. 336-338.
  28. "On discrete variables whose sum is absolutely continuous," Ann. Math. Stat., Vol. 28, No. 2 (1957), pp. 520-521.
  29. "Design for the control of selection bias," Ann. Math. Stat., Vol. 28, No. 2 (1957), pp. 449-460 (with J.L. Hodges, Jr.).
  30. "On the identifiability problem for function of finite Markov chains," Ann. Math. Stat., Vol. 28, No. 4 (1957), pp. 1011-1015 (with L. Koopmans).
  31. "The entropy of functions of finite-state Markov chains," Trans. First Prague Conference on Information Theory, Decision Functions, and Random Processes, Prague, 1957, pp. 13-20.
  32. "Another countable Markov Process with only instantaneous states," Ann. Math. Stat., Vol. 29, No. 1 (1958), pp. 313-316.
  33. "Proof of Shannon's transmission theorem for finite-state indecomposable channels," Ann. Math. Stat., Vol. 29, No. 4 (1958), pp. 1209-1220 (with L. Breiman and A.J. Thomasian).
  34. "The probability in the extreme tail of a convolution," Ann. Math. Stat., Vol. 30, No. 4 (1959), pp. 1113-1120 (with J.L. Hodges, Jr.).
  35. "The capacity of a class of channels," Ann. Math. Stat., Vol. 30, No. 4, (1959), pp. 1229-1241 (with L. Breiman and A.J. Thomasian).
  36. "Infinite codes for memoryless channels," Ann. Math. Stat., Vol. 30, No. 4, (1959), pp. 1242-1244.
  37. "The capacities of certain channel classes under random coding," Ann. Math. Stat., Vol. 31, No. 3, (1960), pp. 558-567 (with L. Breiman and A.J. Thomasian).
  38. "On the completeness of order statistics," Ann. Math. Stat., Vol. 31, No. 3, (1960), pp. 794-797 (with C.B. Bell and L. Breiman).
  39. "On the functional equation of dynamic programming," Jour. Math. Analysis and Applications, Vol. 2, No. 2 (1961), pp. 273-276.
  40. "Minimax and irreducible matrices," Jour. Math. Analysis and Applications, Vol. 3, No. 1 (1961), pp. 37-39.
  41. "Exponential error bounds for finite-state channels," Proc. Fourth Berkeley Symposium on Math. Stat. and Prob., University of California Press, Vol. 1, (1961), pp. 57-63.
  42. "Discrete dynamic programming," Ann. Math. Stat., Vol. 33, No. 2 (1962), pp. 719-726.
  43. "Merging of opinions with increasing information," Ann. Math. Stat., Vol. 33, No. 3 (1962), pp. 882-886 (with L.E. Dubins).
  44. "A converse to the dominated-convergence theorem," Ill. Jour. of Math., Vol. 7, No. 3 (1963), pp. 508-514 (with L.E. Dubins).
  45. "Non-existence of everywhere proper conditional distributions," Ann. Math. Stat., Vol. 34, No. 1 (1963), pp. 223-225 (with C. Ryll-Nardzewski).
  46. "Sharp bounds on the distribution of the Hardy-Littlewood maximal function," Proc. Amer. Math. Soc., Vol. 14, No. 3 (1963) pp. 450-453 (with L.E. Dubins).
  47. "Memoryless strategies in finite-state dynamic programming," Ann. Math. Stat., Vol. 35, No. 2 (1964), pp. 863-865.
  48. "The tail ¢-field of a Markov chain and a theorem of Orey," Ann. Math. Stat., Vol. 35, No. 3 (1964), p. 1344 (with D. Freedman).
  49. "The last return to equilibrium in a coin tossing game," Ann. Math. Stat., Vol. 35, No. 3 (1964), p. 1344 (with P. Deuel and D. Freedman).
  50. "A remark on the coin tossing game," Ann. Math. Stat., Vol. 35, No. 3 (1964), pp. 1345-1347 (with D. Freedman).
  51. "Probability bounds via dynamic programming, Stochastic processes in Mathematical Physics and Engineering," Proc. of Symposia in Applied Math., Vol. 16, (1964), pp. 277-280.
  52. "The Martin boundary for Polya's urn scheme," Jour. of Applied Prob., Vol. 1, Nos. 1 and 2 (1964), pp. 284-296 (with D.G. Kendall).
  53. "Discounted dynamic programming, "Ann. Math. Stat., Vol. 36, No. 1 (1965), pp. 226-235.
  54. "Positive dynamic programming," Proc. of the Fifth Berkeley Symposium on Math. Stat. and Prob., Vol. 1, Los Angeles and Berkeley, University of California Press, 1966, pp. 415-418.
  55. "A note on Bayes estimates," Ann. Math. Stat., Vol. 38 (1967), pp. 1907-1912 (with P. Bickel).
  56. "Infinite games and analytic sets," Proc. Nat. Acad. Sci., Vol. 58, No. 5 (1967), pp. 1836-1837.
  57. "Elementary path counts," Amer. Math. Monthly, Vol. 74, No. 7 (1967), pp. 801-804 (with J.L. Hodges, Jr.).
  58. "An elementary proof of an identity of Gould's," Reimpreso de Boletin de la Sociedad Matematica Mexicana, Vol. 11, No. 2 (1968), pp. 108-110 (with L. Dubins).
  59. "The big match," Ann. Math. Stat., Vol. 39, No. 1 (1968), pp. 159-163 (with T.S. Ferguson).
  60. "A Borel set not containing a graph," Ann. Math. Stat., Vol. 39, No. 4 (1968), pp. 1345-1347.
  61. "On the local behavior of Markov transition probabilities," Ann. Math. Stat., Vol. 39, No. 6 (1968), pp. 2123-2127, (with D. Freedman).
  62. "Infinite G games with imperfect information," Zastosowania Matematyki Aplicationes Matematicae, Vol. 10, Hugo Steinhaus Jubilee Volume (1969), pp. 99-101.
  63. "On stationary policies," J. Royal Stat. Soc., Vol. 133, Part 1 (1970), pp. 33-37.
  64. Basic Statistics, McGraw-Hill Publishers, New York, 1970, 143pp. (Book).
  65. "Ferguson distributions via Polya urn schemes," Ann. Statist., Vol. 1 (1973), pp. 353-355 (with J.B. MacQueen).
  66. "Discreteness of Ferguson selections," Ann. Statist., Vol. 1 (1973), pp. 356-358.
  67. "On the amount of variance needed to escape from a strip," Ann. Prob., Vol. 1 (1973), pp. 772-787 (with D. Freedman).
  68. "The optimal reward operator in dynamic programming," Ann. Prob., Vol. 2 (1974), pp. 926-941 (with D. Freedman and M. Orkin).
  69. "On existence and non-existence of proper, regular conditional distributions," Ann. Prob., Vol. 3 (1975), pp. 741-752 (with L. Dubins).
  70. "The stochastic processes of Borel gambling and dynamic programming," Ann. Statist., Vol. 4 (1976), pp. 370-374.
  71. "Borel-programmable functions," Ann. Prob., Vol. 6 (1978), pp. 321-324.
  72. There are no Borel SPLIFs. Ann. Prob., Vol. 8 (1980), pp. 1189-1190.
  73. Borel sets via games. Ann. Prob., Vol. 9 (1981), pp. 321-322.
  74. A Bayes but not classically sufficient statistics. Ann. Statist., Vol. 10 (1982), pp. 1025-1026 (with R.V. Ramamoorthi).
  75. A hypothesis-testing game without a value. Festschrift for Erich L. Lehmann, Wadsworth, 1982.
  76. An extension of Skorohod's almost sure representation theorem. Proc. Amer. Math. Soc., Vol. 89 (1983), pp. 691-692, (with Lester Dubins).
  77. Factorization of probability measures and absolutely measureable sets. Proc. Amer. Math. Soc., Vol. 92, (1984), pp. 251-254 (with Ashok Maitra).
  78. Ulam's redistribution of energy problem: collision transformations. Letters in Mathematical Physics, Vol. 10 (1985), pp. 149-153, (with R. Daniel Mauldin).
  79. Stationary plans need not be uniformly adequate for leavable, Borel gambling problems. Proc. Amer. Math. Soc., Vol. 102, (1988), pp. 1024-1027 (with S. Ramakrishnan).
  80. Operator solution of infinite G games of imperfect information. Probability, Statistics and Mathematics. Papers in Honor of Samuel Karlin, pp. 83-87. Academic Press.

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