Skip to main content
Log in

A. A. Markov's work on probability

  • Published:
Archive for History of Exact Sciences Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Abbreviations

IAN :

Izvestia Akad. Nauk, ser. 5 (up to 1906 inclusive) or 6 (from 1907). French subtitle: Bull. Acad. Sci. Up to 1917 the Akademia was called Petersburg Academy, and, from 1917 to 1925, Russian Academy

JMNP :

Zhurnal Ministerstva narodnogo prosveshchenia (J. Ministry people's educ.)

Kasan Bull. :

Izvestia phys.-math. Obschchestva Kasan Univ. (French subtitle: Bull. Soc. phys.-math. Kasan), ser. 2

Kharkow Comm. :

Soobshchenia Kharkow math. obshchestva (French subtitle: Communications Soc. math. Kharkow), ser. 2

MS :

Matematichesky zbornik

References

  1. A. A. Markov Theory of probability. Petersburg, 1884. A lithographic edition, in Russian.

  2. A. A. Markov A note on calculating the probable turnovers of a pension fund, etc., Petersburg, 1884, in Russian.

  3. A. A. Markov Table des valeurs de l'intégrale \(\int\limits_\infty ^\infty {\exp {\text{ (}} - t^{\text{2}} )}\) exp (−t2) dt. Pétersbourg, 1888.

  4. Sur les racines de l'équation exp (x 2) d m exp (−x 2)/dx m=0. IAN, t. 9, No. 5, 1898, 435–446. Russ. transl. [47, pp. 253–269].

    Google Scholar 

  5. A. A. Markov The law of large numbers and the method of least squares (1899) [47, pp. 231–251]. In Russian.

  6. A. A. Markov A note on the problems considered by the fourth auditing commission etc. No place, no date [1899]. In Russian.

  7. Réponse [to Nekrasov's article [92]]. Kasan Bull., t. 9, No. 3, 1899, 41–43, in Russian.

    Google Scholar 

  8. A. A. Markov Application des fonctions continues au calcul des probabilités. Ibid., No. 2, 29–34, in Russian.

  9. A. A. Markov Calculus of probability. Petersburg, 1900. In Russian. Subsequent editions: 1908, 1913 and 1924. Markov, who died in 1922, had time to prepare the last edition which also includes an essay [48] on Markov's life and work. The German translation of the edition of 1908 by H. Liebmann (Wahrscheinlichkeitsrechnung. Leipzig-Berlin, 1912) contains as appendices (German translations of) three of Markov's articles [4; 19; 22]. The translations of both the textbook and the articles differ somewhat from their original versions. The last section of the textbook (pp. 487–581 of the edition of 1924) was added in 1913 and is also available, again in a somewhat different version, in French: Démonstration du second théorème-limite, etc., Pétersbourg, 1913.

  10. Sur une probabilité a posteriori. Kharkow Comm., t. 7, No. 1, 1900, 23–25 (in Russian).

    Google Scholar 

  11. A. A. Markov [Opinions on the proposed answer by Petersburg University to questions on the new statutes of universities.] Coauthors: N. E. Vvedensky et al. Petersburg, 1901. In Russian, published as a manuscript.

  12. A l'occasion de la ruine de joueurs. Kasan Bull., t. 13, No. 1, 1903, 38–45, in Russian.

    Google Scholar 

  13. A. A. Markov Debates in the First [phys.-math.] Department of the Academy of Sciences on the election of B. B. Golytzin to full member of the Academy. Petersburg, 1903. In Russian. (Speeches by five academicians, including Markov.)

  14. A. A. Markov On the solidity of glass. Unpubl., 8 pp., in Russian. [1903.]

  15. A. A. Markov Extension de la loi de grands nombres etcc (1906) [47, pp. 339–361], in Russian.

  16. Recherches sur un cas remarquable d'épreuvres dépendantes (1907). Slightly different French version: Acta math., t. 33, 1910, 87–104.

    Google Scholar 

  17. Sur quelques cas des théorèmes sur les limites de probabilité et des espérances mathématiques. IAN, t. 1, No. 16, 1907, 707–714, in Russian.

    Google Scholar 

  18. Sur quelques cas du théorème sur la limite de probabilité. IAN, t. 2, No. 6, 1908, 483–496, in Russian.

    Google Scholar 

  19. A. A. Markov L'extension des théorèmes limites du calcul des probabilités, etc. (1908) [47, pp. 363–397], in Russian.

  20. A. A. Markov Recherches sur le cas général d'épreuves liées en chaîne (1910) [47, pp. 465–507], in Russian.

  21. A. A. Markov Calculus of finite differences. Odessa, 1910. Second ed. In Russian.

  22. A. A. Markov Sur les valeurs liées qui ne forment pas une chaîne véritable (1911) [47, pp. 399–416], in Russian.

  23. A. A. Markov On the basic principles of the calculus of probability and on the Law of Large Numbers. [100, pp. 149–153]. Orig. publ. in Russian in 1977.

  24. A. A. Markov Sur un cas d'épreuves liées en chaîne multiple (1911) [47, pp. 417–436], in Russian.

  25. A. A. Markov Sur les épreuves liées en chaîne par les événements laissés sans observation (1912) [47, pp. 437–463], in Russian.

  26. Réponse à M. Nekrassov. MS, t. 28, No. 2, 1912, 215–227, in Russian.

    Google Scholar 

  27. Essai d'une recherche statistique sur le texte du roman “Eugène Onegin”, etc., IAN, t. 7, No. 3, 1913, 153–162, in Russian.

    Google Scholar 

  28. A. A. Markov The Bicentennial of the Law of Large Numbers. [100, pp. 158–163]. Orig. publ. in Russian in 1977.

  29. Sur la probabilité a posteriori. [Second note.] Kharkow Comm., t. 14, No. 3, 1914, 105–112, in Russian.

    Google Scholar 

  30. A. A. Markov Sur le problème de J. Bernoulli (1914) [47, pp. 509–521], in Russian.

  31. On teaching mathematics etc. JMNP, t. 56. No. 3, 1915, pp. 126–130 of section on people's education, in Russian.

    Google Scholar 

  32. On P. S. Florov & P. A. Nekrasov's draft etc. JMNP, t. 57, No. 5, 1915, 26–34 of section on current chronicle, in Russian.

    Google Scholar 

  33. A. A. Markov Sur un problème de Laplace (1915) [47, pp. 549–571], in Russian.

  34. Sur l'application de la méthode des ésperances mathématiques aux sommes liées. IAN, t. 9, No. 14, 1915, 1453–1484, in Russian.

    Google Scholar 

  35. A. A. Markov Seminarists and students of non-classical high schools. Newspaper Den, 11 Aug. 1915, p. 3. In Russian.

  36. A. A. Markov Letter to the editor. Ibid., 28 Oct. 1915, p. 3. In Russian.

  37. Rapport de la Commission concernant certaines questions de l'enseignement mathématiques dans l'école secondaire. IAN, t. 10, No. 2, 1916, 66–80, in Russian. The Commission was drawn up from members of the Academy of Sciences and included Markov.

    Google Scholar 

  38. A. A. Markov Sur le coefficient de la dispersion (1916) [47, p.p 523–535], in Russian.

  39. A. A. Markov On the coefficient of dispersion for small numbers. Strakh. Obosrenie, No. 2, 1916, 55–59, in Russian.

  40. Sur une application de la méthode statistique. IAN, t. 10, No. 4, 1916, 239–243, in Russian.

    Google Scholar 

  41. A. A. Markov Sur quelques formules limites du calcul des probabilités (1917) [47, pp. 573–585], in Russian.

  42. Sur quelques questions du calcul des probabilités. IAN, t. 12, No. 18, 1918, 2101–2116, in Russian.

    Google Scholar 

  43. A. A. Markov Généralisation du problème de l'échange successif des boules (1918) [47, pp. 587–595], in Russian.

  44. A. A. Markov Sur le coefficient de la dispersion (Note seconde) (1922) [47, pp. 537–547], in Russian.

  45. La difficulté de la méthode des moments; deux exemples de sa solution incomplète. IAN, t. 16, No. 1–18, 1922 (1924), 281–286, in Russian.

    Google Scholar 

  46. Sur les ellipsoides (ellipses) de dispersion et sur la corrélation. IAN, t. 18, No. 1–11, 1924, 117–126, in Russian.

    Google Scholar 

  47. A. A. Markov Selected works. Ed. Yu. V. Linnik. Leningrad, 1951. In Russian.

Other Authors

  1. Besikovitch, A. S., A biographic essay [on A. A. Markov] [9, 1924, pp. iii–xiv], in Russian.

  2. Bernstein, S. N., Sur l'extension du théorème limite du calcul des probabilites, etc. Math. Annalen, Bd. 97, 1926, 1–59. Russ. transl.: Coll. works, vol. 4. Moscow, 1964, 121–176.

  3. Bernstein, S. N., On P. L. Chebyshev's work on the theory of probability (1945). Coll. Works, vol. 4, 409–433. In Russian.

    Google Scholar 

  4. Bernstein, S. N., Theory of probability, 4th ed. Moscow-Leningrad, 1946. In Russian.

  5. Bortkewitsch, L., Kritische Betrachtungen zur theoretischen Statistik. Jhrb. Nat.-Ökon. u. Stat., 3. Folge, Bd. 10, 1895, 321–360 [pt. 2].

    Google Scholar 

  6. Bortkewitsch, L., Das Gesetz der kleinen Zahlen. Leipzig, 1898.

  7. Brush, S. G., A history of random processes. 1. Brownian movement, etc. (1968). In: Stud. Hist. Stat. and Prob., vol. 2. London, 1977, Eds. M. G. Kendall & R. L. Plackett, 347–382.

  8. Buniakovsky, V. Ya., Elements of the mathematical theory of probability. Petersburg, 1846. In Russian.

  9. Chebyshev, P. L., Des valeurs moyennes. J. math. pures et appl., sér. 2, t. 12, 1867, 177–184. Simult. publ. in Russian.

    Google Scholar 

  10. Chebyshev, P. L., Sur deux théorèmes relatifs aux probabilités. Acta math., t. 14, 1891, 305–315. Orig. publ. in Russian in 1887.

    Google Scholar 

  11. Chebyshev, P. L., Theory of probability. Lectures delivered in 1879–1880. Moscow-Leningrad, 1936. In Russian.

  12. Chuprov, A. A., Essays on the theory of statistics (1909). Moscow, 1959. In Russian.

  13. Chuprov, A. A., Sur l'espérance mathématique du coefficient de divergence. IAN, t. 10, No. 18, 1916, 1789–1798, in Russian.

    Google Scholar 

  14. Chuprov, A. A., Zur Theorie der Stabilität statistischer Reihen. Skand. aktuarietidskr., No. 3–4, 1918, 199–256.

  15. Cournot, A. A., Exposition de la théorie des chances et des probabilités (1843). Paris, 1984.

  16. Dutka, J., On the problem of random flights. Arch. Hist. Exact Sci., vol. 32, Nos. 3–4, 1985, 351–375.

    Google Scholar 

  17. Ehrenfest, P., & T. Ehrenfest, Über zwei bekannte Einwände gegen das Boltzmannsche H-Theorem (1907). In: Ehrenfest, P., Coll. scient, papers. Amsterdam, 1959, 146–149.

  18. Ellis, R. L., On the method of least squares (1844). In author's Math. and other writings. Cambridge, 1863, 12–37.

  19. Emeliakh, L. I., The case of A. A. Markov's excommunication from the church. Voprosy istorii religii i ateisma, vol. 2, Moscow. 1954, 397–411, in Russian.

    Google Scholar 

  20. Ermolaeva, N. S., On P. L. Chebyshev's unpublished course in the theory of probability. First Intern. Congr. Bernoulli Soc., Theses, vol. 2, Moscow, 1986, p. 918. In Russian.

    Google Scholar 

  21. Fletcher, A., et al., An index of mathematical tables, vol. 1. Oxford, 1962.

  22. Galloway, T., A treatise on probability. Edinburgh, 1839.

  23. Gnedenko, B. V., & O. B. Sheynin, Theory of probability. In: Math. of the 19th century. Eds. A. N. Kolomogorov & A. P. Youshkevitch. Moscow, 1978, 184–240. In Russian.

  24. Grodsensky, S. Ya., Chess in the life of scientists. Ed. A. A. Markov, Jr., Moscow, 1983. In Russian.

  25. Günther, N., L'oeuvre pédagogique de A. Markov. IAN, t. 17, No. 1–18, 1923, 35–44, in Russian.

    Google Scholar 

  26. Hagen, G., Grundzüge der Wahrscheinlichkeitsrechnung (1837). Berlin, 1867.

  27. Heiss, K.-P., & W. Lexis. Intern. Enc. Stat., vol. 1. Eds. W. H. Kruskal & Judith M. Tanur. New York-London, 1978, 507–512.

  28. Heyde, C. C., & E. Seneta, I. J. Bienaymé. New York a.o., 1977.

  29. Idelson, N. I., Method of least squares, etc., Moscow, 1947. In Russian.

  30. Kolomogorov, A. N., The role of Russian science in the development of the theory of probability. Uch. zap. Moscow Univ., No. 91, 1947, 53–64, in Russian.

  31. Kolmogorov, A. N., Commentary to Chebyshev's paper [57]. In: Chebyshev's Complete works, vol. 3, Moscow-Leningrad, 1948, 404–409. In Russian.

  32. Lexis, W., Über die Theorie der Stabilität statistischer Reihen (1879). In author's Abh. zur Theorie der Bevölkerungs- und Moralstatistik. Jena, 1903, 170–212.

  33. Liapunov, A. M., Sur une proposition de la théorie des probabilités. IAN, t. 13, No. 4, 1900, 359–386.

    Google Scholar 

  34. Liapunov, A. M., Nouvelle forme du théorème sur la limite de probabilité. Zapiski Acad. Sci. Pétersbg., cl. phys.-math., Sér. 8, t. 12, No. 5, 1901, pp. 24.

    Google Scholar 

  35. Liapunov, A. M., Reply to P. A. Nekrasov. Zapiski Kharkow Univ., t. 3, 1901, 51–63, in Russian.

    Google Scholar 

  36. Linnik, Yu. V., et al., An essay on A. A. Markov's works on the theory of numbers and the theory of probability [47, pp. 614–640], in Russian.

  37. Linnik, Yu. V., et al., Commentaries on A. A. Markov's works on the theory of probability [47, pp. 654–678], in Russian.

  38. Maievsky, N., An exposition of the method of least squares. Petersburg, 1881. In Russian.

  39. Maistrov, L. E., Probability theory. New York-London, 1974. Orig. publ. in Russian in 1967.

  40. Markov, A. A.. Jr., The life of A. A. Markov, Sr. [47, pp. 599–613]. In Russian.

  41. The minutes of the Council of the Petersburg University, issue No. 61. Petersburg, 1905 (1906). In Russian.

  42. Nekrasov, P. A. (All publications are in Russian) Lagrange's series, etc. MS, t. 12, 1885, 49–188, 315–376, 483–578, 643–724.

    Google Scholar 

  43. Nekrasov, P. A., Theory of probability. Lectures delivered in 1887–1888. No place, no date. Lithographic edition. Subsequent editions: 1894 (lithographic), 1896 and 1912 (typographically printed textbooks).

  44. Nekrasov, P. A., Propriétés générales des phénomènes nombreux indépendants, etc. MS, t. 20, No. 3, 1898, 431–442.

    Google Scholar 

  45. Nekrasov, P. A., A l'occasion du mémoire de A. Markof. Kasan Bull., t. 9, No. 1, 1899, 18–26.

    Google Scholar 

  46. Nekrasov, P. A., Nouveaux fondements de la théorie des probabilités des sommes et des moyennes. MS, t. 21, 1900, 579–763; t. 22, 1901, 1–142, 323–498; t. 23, 1902, 41–455.

    Google Scholar 

  47. Nekrasov, P. A., Statistical concentrations and the free causal relationship. JMNP, t. 27, No. 5, 1910, pp. 207–211 of the section on critique and bibliography.

    Google Scholar 

  48. Nekrasov, P. A., Sur les fondements de la loi des grands nombres, etc. MS, t. 27, No. 4, 1911, 433–451.

    Google Scholar 

  49. Nekrasov, P. A., La théorie de Laplace de la méthode des moindres carrés, etc., MS, t. 28, No. 2, 1912, 228–234; t. 29, No. 2, 1914, 190–191.

    Google Scholar 

  50. Nekrasov, P. A., The theory of probability and mathematics in secondary school. JMNP, 1915, section on current chronicle, t. 55, No. 2, 65–127; t. 56, No. 3, 1–43, No. 4, 94–125.

    Google Scholar 

  51. Nekrasov, P. A., The secondary school, etc., Petrograd, 1916.

  52. Neyman, J., Review of book [100]. Hist. Math., vol. 5, No. 4, 1978, 485–486.

  53. Ondar, Kh. O., ed., The correspondence between A. A. Markov and A. A. Chuprov. New York etc., 1981. Orig. publ. in Russian in 1977.

  54. Ondar, Kh. O., A review of the correspondence between A. A. Markov and A. A. Chuprov. [100, pp. 136–145].

  55. Poincaré, H., Calcul des probabilités. Paris, 1896 et 1912.

  56. Poincaré, H., Réflexions sur le calcul des probabilités. Rev. gén. sci. pures et appl., t. 10, 1899, 262–269.

    Google Scholar 

  57. Poincaré, H., La science et l'hypothèse (1902). Paris, 1923.

  58. Poincaré, H., Science et méthode (1908). Paris, 1914.

  59. Poisson, S.-D., Recherches sur la probabilité des jugements etc. Paris, 1837. German transl.: Braunschweig, 1841.

    Google Scholar 

  60. Poisson, S.-D., Sur la probabilité des résultats moyens des observations. Conn. temps pour 1827 (1824), 273–302.

    Google Scholar 

  61. Pólya, G., Wahrscheinlichkeitsrechnung, etc. In: Handb. der biol. Arbeitsmethoden. Hrsg., E. Abderhalden. Abt. 5, Tl. 2. Berlin-Wien, 1928, 669–758.

  62. Posse, K. A., A few words about P. A. Nekrasov's article [of 1915]. JMNP, t. 59, No. 9, 1915, pp. 71–76 of section on current chronicle.

    Google Scholar 

  63. Romanovskii, V. I., Généralisation d'une inégalité de Markoff. C. r. Acad. sci. Paris, t. 180, 1925, 1468–1470. Simult. publ. in Russian.

    Google Scholar 

  64. Romanovskii, V. I., Mathematical statistics, vol. 1. Tashkent, 1961. In Russian. First ed.: 1938.

  65. Seneta, E., Least squares in prerevolutionary Russia. First Austr. Conf. hist. Math. 1980. Clayton, 1981, 168–174.

  66. Seneta, E., The central limit theorem and linear least squares in prerevolutionary Russia, etc., Math. Scientist, vol. 9, 1984, 37–77.

    Google Scholar 

  67. Sheynin, O. B., P. S. Laplace's work on probability. Arch. Hist. Exact Sci. vol. 16, No. 2, 1976, 137–187.

    Google Scholar 

  68. Sheynin, O. B., Laplace's theory of errors. Arch. Hist. Exact Sci. vol. 17, No. 1, 1977, 1–61.

    Google Scholar 

  69. Sheynin, O. B., S.-D. Poisson's work in probability. Arch. Hist. Exact Sci. vol. 18, No. 3, 1978, 245–300.

    Google Scholar 

  70. Sheynin, O. B., C. F. Gauss and the theory of errors. Arch. Hist. Exact Sci. vol. 20, No. 1, 1979, 21–72.

    Google Scholar 

  71. Sheynin, O. B., On the history of medical statistics. Arch. Hist. Exact Sci. vol. 26, No. 3, 1982, 241–286.

    Google Scholar 

  72. Sheynin, O. B., On the history of the statistical method in astronomy. Arch. Hist. Exact Sci. vol. 29, No. 2, 1984, 151–199.

    Google Scholar 

  73. Sheynin, O. B., A. Quetelet as a statistician. Arch. Hist. Exact Sci. vol. 36, No. 4, 1986, 281–325.

    Google Scholar 

  74. Sheynin, O. B., J. Bernoulli and the beginnings of the theory of probability. In: Bernoulli, J., On the law of large numbers. Moscow, 1986, 83–115. In Russian.

  75. Slutsky, E. E., The theory of correlation. Kiev, 1912. In Russian.

  76. Slutsky, E. E., On the logical foundations of the calculus of probability (1925). Selected Works, Moscow, 1960, 18–24. In Russian.

  77. Stigler, S. M., The history of statistics. Cambridge (Mass.)-London, 1986.

  78. Tikhomandritsky, M. A., A course in the theory of probability. Kharkov, 1898. In Russian.

  79. Vasiliev, A. V., The theory of probability. Kasan, 1885. A lithographic edition, in Russian.

  80. Weyl, H., Über der Gleichverteilung von Zahlen mod. 1 (1916). Ges. Abh., Bd 1. Berlin etc., 1968, 563–599.

    Google Scholar 

  81. Yaroshenko, S. P., On the theory of the method of least squares. Zapiski Novoross. Univ., vol. 58, 1893, 193–208 of the second section.

    Google Scholar 

  82. Youshkevitch, Al. Ad., Markov. Dict. Scient. Biogr., vol. 9. New York, 1974. Ed., C. C. Gillispie, 124–130.

    Google Scholar 

  83. Zhukovsky, N. Ye., On the form of ships (1890). Coll. works, vol. 2. Moscow-Leningrad, 1949, 627–639. In Russian.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by H. Freudenthal

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sheynin, O.B. A. A. Markov's work on probability. Arch. Hist. Exact Sci. 39, 337–377 (1989). https://doi.org/10.1007/BF00348446

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00348446

Navigation