The origin of infinitely divisible distributions: from de Finetti’s problem to Lévy-Khintchine formula
نویسندگان
چکیده
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, Lévy 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.
منابع مشابه
Brief tutorial of Lévy processes
Some fundamental properties related to Lévy processes are discussed. Topics include infinitely divisible distributions, Lévy-Khintchine formula, Poisson random measures, Lévy-Itô decomposition, series representations, and density transformations. 1 Basic properties • In short, a Lévy process X = {Xt}t≥1 is a R-valued process with independent and stationary increments whose paths are right-conti...
متن کاملRepresentation of infinitely divisible distributions on cones
We investigate infinitely divisible distributions on cones in Fréchet spaces. We show that every infinitely divisible distribution concentrated on a normal cone has the regular Lévy–Khintchine representation if and only if the cone is regular. These results are relevant to the study of multidimensional subordination.
متن کاملConstruction of Lévy Drivers for Financial Models
We extend the Lévy-Khintchine representation for an infinitely divisible distribution to define a driving process in the context of the bond price framework developed earlier. We describe a methodology using subordination to construct such processes and we develop some examples in detail.
متن کاملModeling of Infinite Divisible Distributions Using Invariant and Equivariant Functions
Basu’s theorem is one of the most elegant results of classical statistics. Succinctly put, the theorem says: if T is a complete sufficient statistic for a family of probability measures, and V is an ancillary statistic, then T and V are independent. A very novel application of Basu’s theorem appears recently in proving the infinite divisibility of certain statistics. In addition ...
متن کاملCharacteristic Kernels and Infinitely Divisible Distributions
We connect shift-invariant characteristic kernels to infinitely divisible distributions on R. Characteristic kernels play an important role in machine learning applications with their kernel means to distinguish any two probability measures. The contribution of this paper is twofold. First, we show, using the Lévy–Khintchine formula, that any shift-invariant kernel given by a bounded, continuou...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006