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We introduce some new indexes to measure the departure of any multivariate continuous distribution on non-negative orthant from a given reference one such the uncorrelated exponential model, similar to the relative Fisher dispersion indexes…

In this paper we study the asymptotic behavior of the (skew) Macdonald and Jack symmetric polynomials as the number of variables grows to infinity. We characterize their limits in terms of certain variational problems. As an intermediate…

We derive an exact formula for the covariance of cartesian distances in two simple polymer models, the freely-jointed chain and a discrete flexible model with nearest-neighbor interaction. We show that even in the interaction-free case…

The aim of this paper is to prove an uncertainty principle for the representation of a vector in two bases. Our result extends previously known qualitative uncertainty principles into quantitative estimates. We then show how to transfer…

Fix an integer k, and let I(l), l=1,2,..., be a sequence of k-dimensional vectors of multiple Wiener-It\^o integrals with respect to a general Gaussian process. We establish necessary and sufficient conditions to have that, as l diverges,…

Stochastic mechanics is regarded as a physical theory to explain quantum mechanics with classical terms such that some of the quantum mechanics paradoxes can be avoided. Here we propose a new variational principle to uncover more insights…

Regular variation is often used as the starting point for modeling multivariate heavy-tailed data. A random vector is regularly varying if and only if its radial part $R$ is regularly varying and is asymptotically independent of the angular…

In this paper, we study large deviation principles of nonlinear filtering for McKean-Vlasov stochastic differential equations. First of all, we establish the large deviation principle for the space-distribution dependent Zakai equation by a…

We obtain the estimate of difference between binomial and generalized binomial distributions in $\chi^2$ metric and in several other related metrics

We consider Borwein-Preiss and Ekeland variational principles using distance functions that neither is symmetric nor enjoy the triangular inequality. All the given results rely exclusively on the convergence and continuity behaviors induced…

It is common for genomic data analysis to use $p$-values from a large number of permutation tests. The multiplicity of tests may require very tiny $p$-values in order to reject any null hypotheses and the common practice of using randomly…

In this paper, we prove the large deviation principle (LDP) for stochastic differential equations driven by stochastic integrals in one dimension. The result can be proved with a minimal use of rough path theory, and this implies the LDP…

(To appear in The American Statistician.) Distance covariance (Sz\'ekely, Rizzo, and Bakirov, 2007) is a fascinating recent notion, which is popular as a test for dependence of any type between random variables $X$ and $Y$. This approach…

In this note we introduce the notion of factorial moment distance for non-negative integer-valued random variables and we compare it with the total variation distance. Furthermore, we study the rate of convergence in the classical matching…

We consider the process of partial sums of moving averages of finite order with a regular varying memory function, constructed from a stationary sequence, variance of the sum of which is a regularly varying function. We study the Gaussian…

This paper is concerned with the general theme of relating the Large Deviation Principle (LDP) for the invariant measures of stochastic processes to the associated sample path LDP. It is shown that if the sample path deviation function…

For a system of partial differential equations that has an extended Kovalevskaya form, a reduction procedure is presented that allows one to use a local (point, contact, or higher) symmetry of a system and a symmetry-invariant conservation…

This paper focuses on generalizing quantiles from the ordering point of view. We propose the concept of partial quantiles, which are based on a given partial order. We establish that partial quantiles are equivariant under order-preserving…

This study investigates the extension of distance variance, a validated spread metric for continuous and binary variables [Edelmann et al., 2020, Ann. Stat., 48(6)], to quantify the spread of general categorical variables. We provide both…

In this paper, we provide a criterion on uniform large deviation principles (ULDP) for stochastic differential equations under locally weak monotone conditions and Lyapunov conditions, which can be applied to stochastic systems with…