This paper illustrates how the use of random set theory can benefit partial identification analysis. We revisit the origins of Manski’s work in partial identification (e.g., Manski (1989, 1990)) focusing our discussion on identification of probability distributions and conditional expectations...

A particle system is a family of i.i.d. stochastic processes with values translated by Poisson points. We obtain conditions that ensure the stationarity in time of the particle system in Rd and in some cases provide a full characterisation of the stationarity property. In particular, a full...

We describe several simulation algorithms that yield random probability distributions with given values of risk measures. In case of vanilla risk measures, the algorithms involve combining and transforming random cumulative distribution functions or random Lorenz curves obtained by simulating...

We introduce a multistable subordinator, which generalizes the stable subordinator to the case of time-varying stability index. This enables us to define a multifractional Poisson process. We study properties of these processes and establish the convergence of a continuous-time random walk to...

In recent years, the econometrics literature has shown a growing interest in the study of partially identified models, in which the object of economic and statistical interest is a set rather than a point. The characterization of this set and the development of consistent estimators and...

It is known that each symmetric stable distribution in is related to a norm on that makes embeddable in Lp([0,1]). In the case of a multivariate Cauchy distribution the unit ball in this norm is the polar set to a convex set in called a zonoid. This work interprets symmetric stable laws using...

The quantisation problem for probability measures aims to represent a measure using a discrete measure supported by a finite set . We consider a similar problem where is a realisation of a finite Poisson point process, the objective function is given by the expected Lp-error, and the constraints...

We define a new stochastic order for random vectors in terms of the inclusion relation for the Aumann expectation of certain random sets. We derive some properties of this order, relate it with other well-known multivariate stochastic convex orders, give a geometrical interpretation in terms of...