相关论文: Stability of Random Sums

Sums of independent, bounded random variables concentrate around their expectation approximately as well a Gaussian of the same variance. Well known results of this form include the Bernstein, Hoeffding, and Chernoff inequalities and many…

We consider smoothing equations of the form $$X ~\stackrel{\mathrm{law}}{=}~ \sum_{j \geq 1} T_j X_j + C$$ where $(C,T_1,T_2,\ldots)$ is a given sequence of random variables and $X_1,X_2,\ldots$ are independent copies of $X$ and independent…

Here we give a necessary and sufficient condition for the convergence to a random max infinitely divisible law from that of a random maximum. We then discuss random max-stable laws, their domain of max-attraction and the associated extremal…

In this paper we propose a method to define the range of stability of fixed points for a variety of discrete fractional systems of the order $0 < \alpha <2$. The method is tested on various forms of fractional generalizations of the…

This study investigated the stability of Hamilton--Jacobi equation on general metric spaces with a perturbation in some whole space. This type of stability appears in the domain perturbation problem. We find that the stability holds when…

We say that a random integer variable $X$ is monotone if the modulus of the characteristic function of $X$ is decreasing on $[0,\pi]$. This is the case for many commonly encountered variables, e.g., Bernoulli, Poisson and geometric random…

For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…

We consider a simple model for multidimensional cone-wise linear dynamics around cusp-like equilibria. We assume that the local linear evolution is either $\mathbf{v}^\prime=\mathbb{A}\mathbf{v}$ or $\mathbb{B}\mathbf{v}$ (with…

Let $\{V_{i,j}; (i,j)\in\N^2\}$ be a two-dimensional array of i.i.d.\ random variables. The limit laws of the sum of independent random products $$ Z_n=\sum_{i=1}^{N_n} \prod_{j=1}^{n} e^{V_{i,j}} $$ as $n,N_n\to\infty$ have been…

The class of $\alpha$-stable distributions is widely used in various applications, especially for modelling heavy-tailed data. Although the $\alpha$-stable distributions have been used in practice for many years, new methods for…

The sum of $N$ sufficiently strongly correlated random variables will not in general be Gaussian distributed in the limit N\to\infty. We revisit examples of sums x that have recently been put forward as instances of variables obeying a…

Let $S$ be the multiplicative semigroup of $q\times q$ matrices with positive entries such that every row and every column contains a strictly positive element. Denote by $(X_n)_{n\geq1}$ a sequence of independent identically distributed…

In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…

Selecting regularization parameters in penalized high-dimensional graphical models in a principled, data-driven, and computationally efficient manner continues to be one of the key challenges in high-dimensional statistics. We present…

Homological stability has shown itself to be a powerful tool for the computation of homology of families of groups such as general linear groups, mapping class groups or automorphisms of free groups. We survey here tools and techniques for…

In statistical physics lately a specific kind of average, called the q-expectation value, has been extensively used in the context of q-generalized statistics dealing with distributions following power-laws. In this context q-expectation…

The question of the local stability of the (replica-symmetric) amorphous solid state is addressed for a class of systems undergoing a continuous liquid to amorphous-solid phase transition driven by the effect of random constraints. The…

Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…

We prove a central limit theorem for random sums of the form $\sum_{i=1}^{N_n} X_i$, where $\{X_i\}_{i \geq 1}$ is a stationary $m-$dependent process and $N_n$ is a random index independent of $\{X_i\}_{i\geq 1}$. Our proof is a…

A popular method for selecting the number of clusters is based on stability arguments: one chooses the number of clusters such that the corresponding clustering results are "most stable". In recent years, a series of papers has analyzed the…