The origin of infinitely divisible distributions: from de Finetti's problem to Levy-Khintchine formula

作者: Francesco Mainardi , Sergei Rogosin

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摘要: The article provides an historical survey of the early contri- butions on infinitely divisible distributions starting from pioneering works de Finetti in 1929 up to canonical forms developed thirties by Kolmogorov, Levy and Khintchine. Particular attention is paid single out personal contributions above authors that were published Italian, French or Russian during period 1929-1938. In Appendix we report translation into English a fundamental paper Khintchine Moscow 1937.

参考文章(81)
Stefan Mittnik, Svetlozar T. Rachev, Stable Paretian Models in Finance ,(2000)
FW Fred Steutel, Infinite divisibility in theory and practice Scandinavian Journal of Statistics. ,vol. 6, pp. 57- 64 ,(1979)
Harald Cramér, Über eine Eigenschaft der normalen Verteilungsfunktion Mathematische Zeitschrift. ,vol. 41, pp. 405- 414 ,(1936) , 10.1007/BF01180430
V. A. Statulevičius, I︠u︡. V. Prokhorov, Limit Theorems of Probability Theory ,(2000)
Sidney Resnick, O. E. Barndorff-Nielsen, Thomas Mikosch, Lévy processes : theory and applications Birkhauser Boston. ,(2001)