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

TL;DR

This paper reviews the historical development of infinitely divisible distributions, highlighting key contributions from de Finetti, Kolmogorov, Levy, and Khintchine from 1929 to 1938, including translations of original works.

Contribution

It provides a detailed historical survey emphasizing original contributions and translations that shaped the understanding of infinitely divisible distributions.

Findings

Historical insights into the development of the Levy-Khintchine formula

Identification of original contributions in multiple languages

Translation of Khintchine's 1937 paper included

Abstract

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