Les processus stochastiques de croissance en biologie

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1. Arley ( N.) : 1943. On the Theory of Stochastic Processes, and their Application to the Theory of Cosmic Radiation (Copenhague). Zbl0060.29204MR13855
2. 1949. On the birth and death process (Skand. Akt. Tidsskrift, p. 21-26). Zbl0041.46806MR31621
3. Arley ( N.) et Borchsenius ( V.) : 1945. On the theory of infinite systems of differential equations, and their application to the theory of stochastic processes and the perturbation theory of quantum mechanics (Acta Math., t. 76, p. 261-322). Zbl0060.29205MR13494
4. Armitage ( P.) : 1951. The statistical theory of bacterial populations subject to mutation [J. Roy. Statist. Soc. (B), sous presse, bibliographie]. Zbl0047.13603MR50864
5. Bailey ( N.T.J.) : 1950. A simple stochastic epidemic (Biometrika, t. 37, p. 193-202). Zbl0038.29104MR38636
6. 1951. On estimating the size of mobile populations from recapture data. (Biometrika, t. 38, p. 293-306). Zbl0044.34502
7. Bartlett ( M.S.) : 1946. Stochastic Processes (conférences inédites). 
8. 1949. Some evolutionary stochastic processes [J. Royal Statist. Soc. (B), t. 11, p. 211-229, 265-266 et 280-281, bibliographie]. Zbl0037.08503MR34976
9. 1951 a. The dual recurrence relation for multiplicative processes (Proc. Cambridge Phil. Soc., t. 47, p. 821-825). Zbl0045.07604MR44065
10. 1951 b. Voir Armitage (I95I). 
11. Bartlett ( M.S.) et Kendall ( D.G.) : 1951. On the use of the characteristic functional in the analysis of some stochastic processes occurring in physics and biology (Proc. Cambridge Phil. Soc., t. 47, p. 65-76). Zbl0042.13802MR39947
12. Bellman ( R.) et Harris ( T.E.) : 1948. On the theory of age-dependent stochastic branching processes (Proc. Nat. Acad. Sc., t. 34, p. 601-604). (Une version plus détaillée paraîtra bientôt). Zbl0041.45604MR27466
13. Bernardelli ( H.) : 1941. Population waves (J. Burma Research Soc., t. 31, p. I-18). 
14. Bhabha ( H.J.) : 1950. On the stochastic theory of continuous parametric systems and its application to electron cascades [Proc. Roy. Soc. London (A), t. 202, p. 301-322]. Zbl0039.13801MR36957
15. Bhabha ( H.J.) et Ramakrishnan ( A.) : 1950. The mean square deviation of the number of electrons and quanta in the cascade theory (Proc. Indian Acad. Sc., t. 32, p. 141-153). Zbl0038.14401MR48741
16. Bochner ( S.) : 1947. Stochastic processes (Ann. of Math., t. 48, p. 1014-1061). Zbl0029.36802MR22322
17. Borel ( É.) : 1942. Sur l'emploi du théorème de Bernouilli pour faciliter le calcul d'une infinité de coefficients. Applications au problème de l'attente à un guichet (C. R. Acad. Sc., t. 214. p. 452-456). Zbl0026.33002MR8126JFM68.0276.01
18. Chitty ( D.) et Leslie ( P.H.) : 1951. The estimation of population parameters from data obtained by means of the capture-recapture method (Biometrika, t. 38, p. 269-292). Zbl0044.34501
19. Cochran ( W.G.) : 1949. The present status of Biometry (2e Congrès intern. de Biométrie, Genève, p. I-19, bibliographie). 
20. Consael ( R.) : 1948. Sur une généralisation du procèssus de Pólya (Bull. Classe des Sc., Acad. Roy. de Belgique, 5e série, t. 34, p. 863-876.). Zbl0033.38801MR29122
21. 1949. Sur quelques processus stochastiques discontinus à deux variables aléatoires (Ibid., t. 35, p. 399-416 et 743-755). Zbl0041.45701MR31217
22. 1950. Sur quelques points de la théorie des processus stochastiques (Ibid., t. 36, p. 870-879). Zbl0041.25202MR40617
23. Cramér ( H.) : 1946. Mathematical Methods of Statistics (Princeton). Zbl0063.01014MR16588
24. Déan ( A.C.R.) et Hinshelwood ( C.N.) : 1952. The applicability of the statistical fluctuation test [Proc. Roy. Soc. London (B), t. 139, p. 236-250]. 
25. De Candolle ( A.) : 1873. Histoire des Sciences et des Savants depuis deux siècles (Genève). Voir p. 388. 
26. Erlang ( A.K.) : 1929. Matemo Tidsskrift (B.), p. 36. 
27. Flller ( W.) : 1939. Die Grundlagen der Volterraschen Theorie des Kampfes ums Dasein in wahrscheinlichkeitstheoretischer Behandlung (Acta Biotheoretica, t. 5, p. II-40). Zbl0021.34002MR690284JFM65.1365.01
28. 1940. On the integrodifferential equations of purely discontinuous Markoff processes (Trans. American Math. Soc.. t. 48, p, 488-515.). Zbl0025.34704MR2697JFM66.0624.02
29. 1941. On the integral equation of renewal theory (Ann. Math. Statist., t. 12, p. 243-267). Zbl0026.23001MR5419JFM67.0370.02
30. 1943. On a general class of « contagious » distributions (Ann. Math. Statist., t. 14, p. 389-400). Zbl0063.01341MR9827
31. 1949. On the theory of stochastic processes, with particular reference to applications (Proc. Ist Berkeley Symposium on Math. Statist. and Probability, p. 403-432, bibliographie). Zbl0039.13702MR27980
32. 1950. An Introduction to Probability Theory and its Applications. t. I, New-York, chap. 11 et 17). Zbl0039.13201
33. 1951. Diffusion processes in genetics (Proc. 2nd Berkeley symposium on Math. Statist. and Probability, p. 227-246, bibliographie). Zbl0045.09302MR46022
34. Finney ( D.J.) : 1947. Errors of estimation in inverse sampling (Nature, London, t. 160, p. 195). Zbl0036.09701
35. 1949. On a method of estimating frequencies (Biometrika, t. 36, p. 233-234). Zbl0033.38904MR34007
36. Finney ( D.J.) et Martin ( L.) : 1951. A re-examination of Rahn's data on the number of genes in bacteria (Biometries, t. 7, p. 133-144). 
37. Fisher ( R.A.) : 1922. On the dominance ratio (Proc. Roy. Soc. Edin., t. 42, p. 321-341). 
38. 1930. The Genetical Theory of Natural Selection (Oxford). JFM56.1106.13
39. Fréchet ( M.) : 1938. Recherches théoriques modernes sur le Calcul des Probabilités, t. II, Paris, (bibliographie). Zbl0018.41301
40. Furry ( W.H.) : 1937. On fluctuation phenomena in the passage of high energy electrons through lead (Phys. Rev., t. 52, p. 569-581). Zbl63.1394.04JFM63.1394.04
41. Galton ( F.) et Watson ( H.W.) : 1874. On the probability of the extinction of families (J. Anthrop. Inst., t. 4, p. 138-144). 
42. Good ( I.J.) : 1949 a. The number of individuals in a cascade process (Proc. Cambridge Phil. Soc., t. 45, p. 360-363 Zbl0035.08501MR29489
43. 1949 b. J. Roy. Statist. Soc. (B). t. 11, p. 271-273 et t. 12, p. I. 
44. 1951. Ibid., t. 13, p. 182-183. 
45. Gray ( J.) et Tocher ( J.F.) : 1902. The ethnology of Buchan, IV. The frequency and pigmentation value of surnames in East Aberdeenshire ( Trans. Buchan Field Club, t. 7). 
46. Grenander ( U.) : 1950. Stochastic processes and statistical inference (Ark. Mat., t. 1, p. 195-277, bibliographie). Zbl0058.35501MR39202
47. Haldane ( J.B.S.) : 1945 a. A labour-saving method of sampling (Nature, London, t. 155, p. 49-50). 
48. 1945 b. On a method of estimating frequencies (Biometrika, t. 33, p. 222-225). Zbl0063.01881MR19900
49. 1949. Some statistical problems arising in genetics [J. Roy. Statist. Soc. (B), t. 11, p. I-9]. Zbl0034.07901MR38635
50. Hammersley ( J.M.) : 1950. Electronic computors and the analysis of stochastic processes (Math. Tables, and Aids to Computation, t. 4, p. 56-57). 
51. Harris ( T.E.) : 1948. Branching processes (Ann. Math. Statist., t. 19, p. 474-494, bibliographie). Zbl0041.45603MR27465
52. 1951. Some mathematical models for branching processes (Proc. 2nd Berkeley Symposium on Math. Statist. and Probability, p. 305-328, bibliographie). Zbl0045.07701MR45331
53. Hartley ( H.O.) et Fitch ( E.R.) : 1951. A chart for the incomplete beta-function and the cumulative binomial distribution (Biometrika, t. 38, p. 423-426). Zbl0043.33702MR48744
54. Immel ( E.R.) : 1951. Problems of estimation and hypothesis-testing in connexion with birth-and-death stochastic processes (Ann. Math. Statist., t. 22, p. 485). 
55. Jánossy ( L.) : 1950. Note on the fluctuation problem of cascades (Proc. Phys. Soc. London (A), t. 63. p. 241-249). Zbl0037.14102
56. Karmel ( P.H.) : 1947. The relations betwen male and female reproduction rates (Population Studies, t. 1, p. 249-274). 
57. 1948 a. The relations between male and female nuptiality in a stable population (Ibid., t. 1, p. 353-387). 
58. 1948 b. An analysis of the sources and magnitude of inconsistencies betwen male and female net reproduction rates in actual populations (Ibid., t. 2, p. 240-273). 
59. Kelly ( C.D.) et Rahn ( O.) : 1932. The growth rate of individual bacterial cells (J. Bacteriol., t. 23, p. 147-153). 
60. Kendall ( D.G.) : 1947. A review of some recent work on discontinuous Markoff processes with applications to biology, physics and actuarial science (J. Roy. Statist. Soc., t. 110, p. 130-137). Zbl0063.03200
61. 1948 a. On the generalised birth-and-death process (Ann. Math. Statist., t. 19, p. I-15). Zbl0032.17604
62. 1948 b. On some modes of population growth leading to R. A. Fisher's logarithmic series distribution (Biometrika, t. 35, p. 6-15). Zbl0030.31601MR26282
63. 1948 c. On the role of variable generation time in the development of a stochastic birth process. (Ibid., t. 35, p. 316-330). Zbl0032.04703MR27977
64. 1949. Stochastic processes and population growth [J. Roy. Statist. Soc. (B), t. 11, p. 230-264, 266-267 et 281-282, bibliographie]. Zbl0038.08803MR34977
65. 1950 a. An artificial realisation of a simple birth-and-death process (Ibid., t. 12, p. 116-119). Zbl0039.15402
66. 1950 b. Random fluctuations in the age-distribution of a population whose development is controlled by the simple birth-and-death process. (Ibid., t. 12. p. 278-285). Zbl0041.26601MR42088
67. 1951. Some problems in the theory of queues (Ibid., t. 13, p. 151-173 et 184-185, bibliographie). Zbl0045.07801MR47944
68. 1952 a. On the choice of a mathematical model to represent normal bacterial growth (Ibid., sous presse). Zbl0046.37002
69. 1952 b. Stochastic processes and bacterial growth (Soc. for Exp. Biol., sous presse.) 
70. Kolmogoroff ( A.) : 1936. Sulla teoria di Volterra della lotta per l'esistenza (Giorn. Ist. Ital. Attuari, t. 7, p. 74-80). Zbl0013.31404JFM62.1263.01
71. Kolmogoroff ( A.), Petrovsky ( I.) et Piscounoff ( N.) : 1937. Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique (Bull. Univ. Etat. Moscou (A), (I), t. 6, p. I-25). Zbl0018.32106
72. Kolmogoroff ( A.) et Dmitriev ( N.A.) : 1947. Branching stochastic processes [C. R. Acad. Sc. U.R.S.S. (N. S.), t. 56, p. 5-8 (anglais)]. Zbl0041.45501MR21264
73. Kolmogoroff ( A.) et Savostyanov ( B.A.) : 1947. The calculation of final probabilities for branching random processes [Ibid., t. 56, p. 783-786 (russe)]. MR22044
74. Lea ( D.E.) et Coulson( C.A.) : 1949. The distribution of the number of mutants in bacterial populations (J. Genetics, t. 49, p. 264-285). 
75. Le Cam : 1947. Un instrument d'étude des fonctions aléatoires : la fonctionnelle caractéristique (C. R. Acad. Sc., t. 224, p. 710-711). Zbl0029.06203MR19862
76. Lederberg ( J.) (sous la direction de) : 1951. Papers in Microbial Genetics (Madison, É.-U.). 
77. Leslie ( P.H.) : 1945. On the use of matrices in certain population mathematics (Biometrika, t. 33, p. 183-212). Zbl0060.31803MR15760
78. 1948. Some further notes on the use of matrices in population mathematics (Ibid., t. 35, p. 213-245). Zbl0034.23303MR27991
79. Lévy ( P.) : 1948. Processus Stochastiques et Mouvement Brownien (Paris), (bibliographie). Zbl0034.22603MR29120
80. Lewis ( E.G.) : 1942. On the generation and growth of a populatiou (Sankhya, t. 6, p. 93-96). 
81. Lotka ( A.J.) : 1931. The extinction of families (J. Washington Acad. Sc., t. 21, p. 377-380 et 453-459). 
82. 1939. Analyse démographique avec application particulière à l'espèce humaine (Acta Sc. Ind., p. 780, Paris). Zbl0021.34004JFM65.1366.02
83. 1945. Population analysis as a chapter in the mathematical theory of evolution (Essays on Growth and Form presented to d'Arcy Wentworth Thompson rédigés par W. E. LE GROS CLARK et P. B. MEDAWAR, Oxford) (bibliographie). Zbl0060.31711MR17508
84. 1948. Application of recurrent series in renewal theory (Ann. Math. Statist., t. 19, p. 190-206). Zbl0031.37302MR26284
85. Luria ( S.E.) et Delbrück ( M.) : 1943. Mutations of bacteria from virus sensitivity to virus resistance (Genetics, t. 28, p. 491-511). 
86. Malécot ( G.) : 1948. Les Mathématiques de l'Hérédité (Paris). Zbl0031.17304MR27490
87. 1949. Les processus stochastiques de la génétique (Coll. intern. du C. N. R. S., t. 13, p. 121-126). Zbl0034.23302MR33510
88. 1950. Quelques schèmes probabilistes sur la variabilité des populations naturelles [Ann. de l'Univ. de Lyon (A), t. 13, p. 37-60]. Zbl0041.46901MR43439
89. Martin ( L.) : 1948-1949. Évolution de la Biométrie (Bull. de l'Inst. Agronom. de Gembloux, t. 17, p. 43-66, bibliographie). 
90. Mc Kendrick ( A.G.) : 1914. Studies on the theory of continuous probabilities, with special reference to its bearing on natural phenomena of a progressive nature (Proc. London Math. Soc., 2e sèrie, t. 13, p. 401-416). Zbl45.1265.03JFM45.0371.11
91. Moran ( P.A.P.) : 1950. Some remarks on animal population dynamics (Biometrics, t. 6, p. 250-258). 
92. 1951 a. Estimation methods for evolutive processes (J. Roy. Statist. Soc. (B), t. 13, p. 141-146). Zbl0045.22804MR45999
93. 1951 b. A mathematical theory of animal trapping (Biometrika, t. 38, p. 307-311). Zbl0043.14404
94. 1952. The Statistical analysis of game-bird records (J. Animal Ecology, t. 21, p. 154-518). 
95. Mourier ( E.) : 1949. Sur l'espérance mathématique d'un élément aléatoire dans un espace de Banach (C. R. Acad. Sc., t. 229, p. 1300-1301). Zbl0034.22301MR32980
96. 1950. Propriétés des caractéristiques d'un élément aléatoire dans un espace de Banach (Ibid., t. 231, p. 28-29). Zbl0039.34802MR36470
97. 1951. Lois des grands nombres et théorie érodique (Ibid., t. 232, p. 923-925). Zbl0042.37603MR39916
98. Moyal ( J.E.) : 1949. J. Roy. Statist. Soc. (B), t. 11, p. 265. MR34975
99. Newcombe ( H.E.) : 1948. Delayed phenotypic expression of spontaneous mutations in Escherichia coli (Genetics, t. 33, p. 447-476, bibliographie). 
100. Otter ( R.) : 1949. The multiplicative process (Ann. Math. Statist., t. 20, p. 206-224). Zbl0033.38301MR30716
101. Palm ( C.) : 1945. Voir Arley et Borchsenius (I945), (p. 298-299). 
102. Park ( T.) : 1948. Experimental studies of interspecies competition, I (Ecol. Monographs, t. 18, p. 265-308). 
103. Pólya ( G.) : 1930. Sur quelques points de la théorie des probabilités (Ann. Inst. H. Poincaré, t. 1, p. 117-161). JFM57.0610.02
104. Prendiville ( B.J.) 1949. J. Roy. Statist. Soc. (B), t. 11, p. 273. 
105. Rahn ( O.) : 1932. A chemical explanation of the variability of the growth rate (J. Gen. Physiol,, t. 15, p. 257-277). 
106. 1934. Chemistry of cell growth, II, (Cold Spring Harbour Symp. on Quantitative Biol., t. 2, p. 63-69). 
107. Ramakrishnan ( A.) : 1950. Stochastic proceeses relating to particles distributed in a continuous infinity of states (Prob. Cambridge Phil. Soc., t. 46, p. 595-602). Zbl0039.13703MR50217
108. 1951. Some simple stochastic processes (J. Royal Statist. Soc. (B), t. 13, p. 131-140). Zbl0045.08001MR45975
109. Savostyanov ( B.A.) : 1948. On the theory of braraching random processes [C. R. Acad. Sc. U. R. S. S., t. 59, p. 1407-1410 (russe)]. MR24090
110. Steffensen ( J.F.) : 1930. Om sandsynligheden for at afkommet uddør (Matem. Tidsskrift (B), p. 19-23). Zbl56.0447.02JFM56.0447.02
111. 1933. Deux problèmes du calcul des probabilités (Ann. Inst. H. Poincaré, t. 3, p. 319-344). Zbl0007.02105JFM59.1176.01
112. Thompson ( W.R.) et Soper ( H.E.) : 1931. On the reproduction of organisms with overlapping generations (Bull. Entom. Research., t. 22, p. 147-172). 
113. Tweedie ( M.C.K.) : 1945. Inverse statistical variates (Nature, London, t, 155, p. 453). Zbl0063.07892MR11907
114. Volterra ( V.) : 1931. Leçons sur la théorie mathématique de la lutte pour la vie (Paris). Zbl0002.04202JFM57.0466.02
115. Wald ( A.) : 1948. Asymptotic properties of the maximum likelihood estimate of an unknown parameter of a discrete stochastic process (Ann. Math. Statist., t. 19, p. 40-46). Zbl0032.17301MR24114
116. Woodward ( P.M.) : 1947. A statistical theory of cascade multiplication (Proc. Cambridge Phil. Soc., t. 44, p. 404-412). Zbl0031.09601MR26283
117. Yaglom ( A.M.) : 1947. Certain limit theorems of the theory of branching random processes (C. R. Acad. Sc. U, R. S. S., t.56, p. 795-798 (russe). Zbl0041.45602MR22045
118. Yule ( G.U.) : 1925. A mathematical theory of evolution [Phil. Trans. Roy. Soc. London (B), t. 213, p. 21-87]. 

1. M.S. Bartlett, Processus stochastiques ponctuels
2. Maurice Girault, Processus ponctuels
3. Paul-Louis Hennequin, Processus de Markoff en cascade