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Categorical random variables are a common staple in machine learning methods and other applications across disciplines. Many times, correlation within categorical predictors exists, and has been noted to have an effect on various algorithm…

Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…

Some partial orderings which compare probability distributions with the expo- nential distribution, are found to be very useful to understand the phenomenon of ageing. Here, we introduce some new generalized partial orderings which de-…

In this paper, we introduce and develop the concept of conditional quantization for Borel probability measures on $\mathbb{R}^k,$ considering both constrained and unconstrained frameworks. For each setting, we define the associated…

In this note we establish some appropriate conditions for stochastic equality of two random variables/vectors which are ordered with respect to convex ordering or with respect to supermodular ordering. Multivariate extensions of this result…

In this article, we demonstrate the common fixed point theorems for three transformations on vector S-metric space by utilizing weakly compatible and point of coincidence. Moreover, some of our results generalize the existing results in the…

Deciding the positivity of a sequence defined by a linear recurrence with polynomial coefficients and initial condition is difficult in general. Even in the case of recurrences with constant coefficients, it is known to be decidable only…

As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…

Contextual situations are those in which seemingly "the same" random variable changes its identity depending on the conditions under which it is recorded. Such a change of identity is observed whenever the assumption that the variable is…

The quantization of vector bundles is defined. Examples are constructed for the well controlled case of equivariant vector bundles over compact coadjoint orbits. (Coadjoint orbits are symplectic spaces with a transitive, semisimple symmetry…

In this paper we study Appell polynomials by connecting them to random variables. This probabilistic approach yields, e.g., the mean value property which is fundamental in the sense that many other properties can be derived from it. We also…

We introduce a category Prob of probability spaces whose objects are all probability spaces and arrows are corresponding to measurable functions satisfying an absolutely continuous requirement. We can consider a Prob-arrow as an evolving…

In the field of categorical probability, one uses concepts and techniques from category theory, such as monads and monoidal categories, to study the structures of probability and statistics. In this paper, we connect some ideas from…

This article presents a deep investigation of fixed points for multivalued weak contractions in cone metric spaces. We extend Berinde weak contraction principles to the multivalued setting in cone metric spaces, developing existence,…

A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…

A class of generalized definitions of expectation value is often employed in nonequilibrium statistical mechanics for complex systems. Here, the necessary and sufficient condition is presented for such a class to be stable under small…

Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in…

The existence and construction of common invariant cones for families of real matrices is considered. The complete results are obtained for 2x2 matrices (with no additional restrictions) and for families of simultaneously diagonalizable…

Many key quantities in statistics and probability theory such as the expectation, quantiles, expectiles and many risk measures are law-determined maps from a space of random variables to the reals. We call such a law-determined map, which…

The aim of this paper is to discuss Penot's problem on a generalization of Caristi's fixed point theorem. We settle this problem in the negative and we present some new theorems on the existence of fixed points of set-valued mappings in…