infinitely divisible laws
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Author(s):  
Anthony G. Pakes

AbstractA family of generalised Planck (GP) laws is defined and its structural properties explored. Sometimes subject to parameter restrictions, a GP law is a randomly scaled gamma law; it arises as the equilibrium law of a perturbed version of the Feller mean reverting diffusion; the density functions can be decreasing, unimodal or bimodal; it is infinitely divisible. It is argued that the GP law is not a generalised gamma convolution. Characterisations are obtained in terms of invariance under random contraction of a weighted version of a related law. The GP law is a particular instance of equilibrium laws obtained from a recursion suggested by a genetic mutation-selection balance model. Some related infinitely divisible laws are exhibited.


2021 ◽  
Vol 66 (4) ◽  
pp. 806-838
Author(s):  
Геннадий Петрович Чистяков ◽  
Gennadii Petrovich Chistyakov ◽  
Фридрих Гeтце ◽  
Friedrich Gotze

Основываясь на методе сyбoрдинационных функций, мы получаем оценки минимальных ошибок аппроксимации $n$-кратных свободных сверток вероятностных мер безгранично делимыми свободными вероятностными мерами.


2020 ◽  
Vol 156 ◽  
pp. 108607
Author(s):  
Arijit Chakrabarty ◽  
Sukrit Chakraborty ◽  
Rajat Subhra Hazra

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Anthony G. Pakes ◽  
S. Satheesh

We discuss the nature of gaps in the support of a discretely infinitely divisible distribution from the angle of compound Poisson laws/processes. The discussion is extended to infinitely divisible distributions on the nonnegative real line.


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