Related papers: On the Li--Zheng theorem

Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the product $XY$ is derived. Some basic distributional properties are also derived, including…

In this article we consider questions related to the behavior of the moments $M_{m}\left( \left\{ z_{j}\right\} \right) $ when the indices are restricted to specific subsequences of integers, such as the even or odd moments. If $n\geq2$ we…

The sensitivity of trajectories over finite time intervals t to perturbations of the initial conditions can be associated with a finite-time Lyapunov exponent lambda, obtained from the elements M_{ij} of the stability matrix M. For globally…

We introduce the notion of a conditionally free product and conditionally free convolution. We describe this convolution both from a combinatorial point of view, by showing its connection with the lattice of non-crossing partitions, and…

We derive two-sided bounds for moments of random multilinear forms (random chaoses) with nonnegative coeficients generated by independent nonnegative random variables $X_i$ which satisfy the following condition on the growth of moments:…

In this paper, we present methods of obtaining single moments of order statistics arising from posibly dependent and non-identically distributed discrete random variables. We derive exact and approximate formulas convenient for numerical…

(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…

It is well known that a Lorenz curve, derived from the distribution function of a random variable, can itself be viewed as a probability distribution function of a new random variable [4]. In a previous work of ours [26], we proved the…

Let $Z$ be a random variable with values in a proper closed convex cone $C\subset \mathbb{R}^d$, $A$ a random endomorphism of $C$ and $N$ a random integer. We assume that $Z$, $A$, $N$ are independent. Given $N$ independent copies…

We say that a random vector $X=(X_1,...,X_n)$ in $R^n$ is an $n$-dimensional version of a random variable $Y$ if for any $a\in R^n$ the random variables $\sum a_iX_i$ and $\gamma(a) Y$ are identically distributed, where $\gamma:R^n\to…

We obtain the law of large numbers (LLN) and the central limit theorem (CLT) for weakly dependent non-stationary arrays of random fields with asymptotically unbounded moments. The weak dependence condition for arrays of random fields is…

The strong law of large numbers for linear combinations of functions of order statistics ($L$-statistics) based on weakly dependent random variables is proven. We also establish the Glivenko--Cantelli theorem for $\phi$-mixing sequences of…

The Poisson distribution is the probability distribution of the number of independent events in a given period of time. Although the Poisson distribution appears ubiquitously in various stochastic dynamics of gene expression, both as…

We consider fixed effects binary choice models with a fixed number of periods $T$ and regressors without a large support. If the time-varying unobserved terms are i.i.d. with known distribution $F$, \cite{chamberlain2010} shows that the…

Let $X_1,...,X_n$ be $n$ independent unbounded real random variables which have common, roughly speaking, light-tailed type distribution. Denote by $S_1^n$ their sum and by $\pi^{a_n}$ the tilted density of $X_1$, where $a_n…

We propose two novel ways of introducing dependence among Poisson counts through the use of latent variables in a three levels hierarchical model. Marginal distributions of the random variables of interest are Poisson with strict…

The paper is divided into two parts. In the first part we lay down the foundation for defining the joint annihilation-preservation-creation decomposition of a finite family of, not necessarily commutative random variables, and show that…

We consider elliptic second order partial differential operators with Lipschitz continuous leading order coefficients on finite cubes and the whole Euclidean space. We prove quantitative sampling and equidistribution theorems for…

This paper concerns about the limiting distributions of change point estimators, in a high-dimensional linear regression time series context, where a regression object $(y_t, X_t) \in \mathbb{R} \times \mathbb{R}^p$ is observed at every…

In this work we address the problem of detecting whether a sampled probability distribution of a random variable $V$ has infinite first moment. This issue is notably important when the sample results from complex numerical simulation…