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In the new field of financial systemic risk, the network of interbank counterparty relationships can be described as a directed random graph. In "cascade models" of systemic risk, this "skeleton" acts as the medium through which financial…
We show that the probability of appearance of synchronisation in chaotic coupled map lattices is related to the distribution of the maximum of a certain observable evaluated along almost all orbit. We show that such distribution belongs to…
Stochastic monotonicity is a well known partial order relation between probability measures defined on the same partially ordered set. Strassen Theorem establishes equivalence between stochastic monotonicity and the existence of a coupling…
Researchers are often interested in drawing inferences regarding the order between two experimental groups on the basis of multivariate response data. Since standard multivariate methods are designed for two-sided alternatives, they may not…
We provide self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem appears to be new but is closely related to results…
We show that a family of random variables is uniformly integrable if and only if it is stochastically bounded in the increasing convex order by an integrable random variable. This result is complemented by proving analogous statements for…
We generalize the classical probability frame by adopting a wider family of random variables that includes nondeterministic ones. The frame that emerges is known to host a ''classical'' extension of quantum mechanics. We discuss the notion…
We prove limit theorems for sums of randomly chosen random variables conditioned on the summands. We consider several versions of the corner growth setting, including specific cases of dependence amongst the summands and summands with heavy…
Recovering causal structure in the presence of latent variables is an important but challenging task. While many methods have been proposed to handle it, most of them require strict and/or untestable assumptions on the causal structure. In…
This work is entirely devoted to compare the largest claims from two heterogeneous portfolios. It is assumed that the claim amounts in an insurance portfolio are nonnegative absolutely continuous random variables and belong to a general…
Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave…
Building on recent developments in models focused on the shape properties of odds ratios, this paper introduces two new models that expand the class of available distributions while preserving specific shape characteristics of an underlying…
There is a duality theory connecting certain stochastic orderings between cumulative distribution functions F_1,F_2 and stochastic orderings between their inverses F_1^(-1),F_2^(-1). This underlies some theories of utility in the case of…
We introduce a quantitative method to compare arbitrary pairs of graph centrality measures, based on the ordering of vertices induced by them. The proposed method is conceptually simple, mathematically elegant, and allows for a quantitative…
The purpose of this paper is to introduce, study and analyze a new stochastic order which lies in the framework of the mean residual life and the combination convexity orders. Several preservation properties of the new order under…
This paper is framed in a series of studies on attraction-repulsion chemotaxis models combining different effects: nonlinear diffusion and sensitivities and logistic sources, for the dynamics of the cell density, and consumption and/or…
Conditional specification of distributions is a developing area with increasing applications. In the finite discrete case, a variety of compatible conditions can be derived. In this paper, we propose an alternative approach to study the…
This paper introduces the order-theoretic concept of lattices along with the concept of consistent quantification where lattice elements are mapped to real numbers in such a way that preserves some aspect of the order-theoretic structure.…
We investigate the physical mechanism behind the counterintuitive phenomenon, the distribution of continuous-variable entanglement between two distant modes by sending a third separable auxiliary mode between them. For this purpose, we…
Mixup is a highly successful technique to improve generalization of neural networks by augmenting the training data with combinations of random pairs. Selective mixup is a family of methods that apply mixup to specific pairs, e.g. only…