On a general probability theorem and its applications in the theory of the stochastic processes
作者： Lajos Takács , W. L. Smith
DOI: 10.1017/S0305004100033375
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摘要: Let us consider an experiment, the possible outcomes of which are random events. A1, A2, …, An be some these outcomes. Define variable ηn as number events occurring simultaneously among in experiment. Denote by Pk = (ηn k) (k 0,1, 2, n), distribution and , binomial moments ηn. Here is symbol probability & that expectation.
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sci-hub.se 参考文章(16)
F. N. David, R. Fortet, Calcul des Probabilités Journal of the Royal Statistical Society: Series A (General). ,vol. 114, pp. 578- 579 ,(1951) , 10.2307/2981094
Maurice Fréchet, Les probabilités associées à un système d'événements compatibles et dépendants Hermann. ,(1940)
Alladi Ramakrishnan, Stochastic processes associated with random divisions of a line Mathematical Proceedings of the Cambridge Philosophical Society. ,vol. 49, pp. 473- 485 ,(1953) , 10.1017/S0305004100028644
W. R. Dean, Note on the Green's function of an elastic plate Mathematical Proceedings of the Cambridge Philosophical Society. ,vol. 50, pp. 623- 627 ,(1954) , 10.1017/S0305004100029753
J. M. Hammersley, On counters with random dead time. I Mathematical Proceedings of the Cambridge Philosophical Society. ,vol. 49, pp. 623- 637 ,(1953) , 10.1017/S0305004100028826
C Levert, W.L Scheen, Probability fluctuations of discharges in a Geiger-Müller counter produced by cosmic radiation Physica D: Nonlinear Phenomena. ,vol. 10, pp. 225- 238 ,(1943) , 10.1016/S0031-8914(43)90039-4
Lajos Takács, On processes of happenings generated by means of a poisson process Acta Mathematica Hungarica. ,vol. 6, pp. 81- 99 ,(1955) , 10.1007/BF02021269
W. L. STEVENS, SOLUTION TO A GEOMETRICAL PROBLEM IN PROBABILITY Annals of Human Genetics. ,vol. 9, pp. 315- 320 ,(1939) , 10.1111/J.1469-1809.1939.TB02216.X
R. A. FISHER, ON THE SIMILARITY OF THE DISTRIBUTIONS FOUND FOR THE TEST OF SIGNIFICANCE IN HARMONIC ANALYSIS, AND IN STEVENS'S PROBLEM IN GEOMETRICAL PROBABILITY Annals of Human Genetics. ,vol. 10, pp. 14- 17 ,(1940) , 10.1111/J.1469-1809.1940.TB02233.X
Kai Lai Chung, On the Probability of the Occurrence of at Least $m$ Events Among $n$ Arbitrary Events Annals of Mathematical Statistics. ,vol. 12, pp. 328- 338 ,(1941) , 10.1214/AOMS/1177731715