A dozen de Finetti-style results in search of a theory
A necessary and sufficient condition for the -coalescent to come down from the infinity.
A population model for -coalescents with neutral mutations.
A -analogue of de Finetti's theorem.
A species sampling model with finitely many types.
Alpha-stable branching and beta-coalescents.
An improved version of a theorem concerning finite row-column exchangeable arrays
We improve a result of Bassan and Scarsini (1998) concerning necessary conditions for finite and infinite extendibility of a finite row-column exchangeable array, and provide a simpler proof for the result.
Bivariate copulas, norms and non-exchangeability
The present paper is related to the study of asymmetry for copulas by introducing functionals based on different norms for continuous variables. In particular, we discuss some facts concerning asymmetry and we point out some flaws occurring in the recent literature dealing with this matter.
Coalescents with simultaneous multiple collisions.
Componentwise concave copulas and their asymmetry
The class of componentwise concave copulas is considered, with particular emphasis on its closure under some constructions of copulas (e.g., ordinal sum) and its relations with other classes of copulas characterized by some notions of concavity and/or convexity. Then, a sharp upper bound is given for the -measure of non-exchangeability for copulas belonging to this class.
Conditional distributions, exchangeable particle systems, and stochastic partial differential equations
Stochastic partial differential equations (SPDEs) whose solutions are probability-measure-valued processes are considered. Measure-valued processes of this type arise naturally as de Finetti measures of infinite exchangeable systems of particles and as the solutions for filtering problems. In particular, we consider a model of asset price determination by an infinite collection of competing traders. Each trader’s valuations of the assets are given by the solution of a stochastic differential equation,...
De Finetti's-type results for some families of non identically distributed random variables.
Exchangeable fragmentation-coalescence processes and their equilibrium measures.
Exchangeable measures for subshifts
Finite row-column exchangeable arrays.
Finite row-column exchangeable arrays
We generalize well known results about the extendibility of finite exchangeable sequences and provide necessary conditions for finite and infinite extendibility of a finite row-column exchangeable array. These conditions depend in a simple way on the correlation matrix of the array.
Fragmentation of ordered partitions and intervals.
Genealogy of flows of continuous-state branching processes via flows of partitions and the Eve property
We encode the genealogy of a continuous-state branching process associated with a branching mechanism – or in short – using a stochastic flow of partitions. This encoding holds for all branching mechanisms and appears as a very tractable object to deal with asymptotic behaviours and convergences. In particular we study the so-called Eve property – the existence of an ancestor from which the entire population descends asymptotically – and give a necessary and sufficient condition on the for...
Infinitely divisible random probability distributions with an application to a random motion in a random environment.
La loi des grands nombres pour une suite échangeable