We study the fair allocation of a one dimensional and infinitely divisible good (money) when individuals have other-regarding preferences. Using only ordinal and non comparable information about such preferences, how should society measure the social welfare associated to any conceivable allocation? In both a model of average and positional externalities, we characterize a class of social prefe...

In this paper, we study the generalization bound for an empirical process of samples independently drawn from an infinitely divisible (ID) distribution, which is termed as the ID empirical process. In particular, based on a martingale method, we develop deviation inequalities for the sequence of random variables of an ID distribution. By applying the obtained deviation inequalities, we then sho...

We consider the problem of allocating infinitely divisible commodities among a group of agents. Especially, we focus on the case where there are several commodities to be allocated, and agents have continuous, strictly convex, and separable preferences. In this paper, we establish that the uniform rule is the only rule satisfying strategy-proofness, unanimity, symmetry, and nonbossiness.

Let us recall some basics on infinitely divisible probability distributions or laws. We denote the set of strictly positive integers by N∗. Definition A distribution G is called infinitely divisible if for all n ∈ N∗ there exists a distribution Gn such that G equals the n-fold convolution of Gn with itself, denoted as (Gn) . In other words, the distribution of a random variable S is infinitely ...

We observe that the function Fα(x) = (1+αx α)e−x α is completely monotone iff α ≤ α0 for some α0 ∈ ]2/3, 3/4[. This property is equivalent to the unimodality of the inverse positive α-stable law. The random variable associated with Fα appears then in two different factorizations of the positive α-stable distribution. Furthermore, it is infinitely divisible iff α ≤ α1 for some α1 ∈ ]2/3, α0[ and...

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 duri...

Abstract: We extend the boson process first to a large class of Cox processes and second an even larger class of infinitely divisible point processes. Density and moment results are studied in detail. These results are obtained in closed form as weighted permanents, so the extension is called a permanent process. Temporal extensions and a particularly tractable case of the permanent process are...

This paper proposes to unify fading distributions by modeling the magnitude-squared of the instantaneous channel gain as an infinitely divisible random variable. A random variable is said to be infinitely divisible, if it can be written as a sum of n ≥ 1 independent and identically distributed random variables, for each n. Infinitely divisible random variables have many interesting mathematical...

The classical duel is a zero-sum game of two players of the following type. The players have certain resources and use them during a given time interval with the goal of achieving success. Use of the resource γ at the moment t leads to success with the probability depending on the amount of resource γ and the time t only (it is usually assumed that the probability of success increases with time...

We give a brief introduction to the class of stochastic processes known as Lévy processes, concentrating principally on their relation with infinitely divisible distributions and the Lévy-Itô decomposition.