相关论文: Stochastically Stable Quenched Measures

Given a closed, convex cone $K\subseteq \mathbb{R}^n$, a multivariate polynomial $f\in\mathbb{C}[\mathbf{z}]$ is called $K$-stable if the imaginary parts of its roots are not contained in the relative interior of $K$. If $K$ is the…

In a companion paper [On semiclassical orthogonal polynomials via polynomial mappings, J. Math. Anal. Appl. (2017)] we proved that the semiclassical class of orthogonal polynomials is stable under polynomial transformations. In this work we…

A finitely generated quadratic module or preordering in the real polynomial ring is called stable, if it admits a certain degree bound on the sums of squares in the representation of polynomials. Stability, first defined explicitly by…

The fidelity between the state of a continuously observed quantum system and the state of its associated quantum filter, is shown to be always a submartingale. The observed system is assumed to be governed by a continuous-time Stochastic…

This work investigates the stability properties of Lyapunov exponents of transfer operator cocycles from a measure-theoretic perspective. Our results focus on so-called Blaschke product cocycles, a class of random dynamical systems amenable…

We prove stochastic stability of chaotic maps for a general class of Markov random perturbations (including singular ones) satisfying some kind of mixing conditions. One of the consequences of this statement is the proof of Ulam's…

We study an infinite class of sequences of sparse polynomials that have binomial coefficients both as exponents and as coefficients. This generalizes a sequence of sparse polynomials which arises in a natural way as graph theoretic…

We study the stability of the mesoscopic fluctuations of certain orthogonal polynomial ensembles on the real line utilizing the recurrence relation of the associated orthogonal polynomials. We prove that under a sparse enough decaying…

In this paper, the problem of stability in terms of two measures is considered for a class of stochastic partial differential delay equations with switching. Sufficient conditions for stability in terms of two measures are obtained based on…

We introduce and study the class of branching-stable point measures, which can be seen as an analog of stable random variables when the branching mechanism for point measures replaces the usual addition. In contrast with the classical…

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…

Quasi-stable ideals appear as leading ideals in the theory of Pommaret bases. We show that quasi-stable leading ideals share many of the properties of the generic initial ideal. In contrast to genericity, quasi-stability is a characteristic…

Estimation of covariance matrices or their inverses plays a central role in many statistical methods. For these methods to work reliably, estimated matrices must not only be invertible but also well-conditioned. In this paper we present an…

Given a stochastic nonlinear system controlled over a possibly noisy communication channel, the paper studies the largest class of channels for which there exist coding and control policies so that the closed-loop system is stochastically…

Measuring the concentration of random variables is a fundamental concept in probability and statistics. Here, we explore a type of concentration measure for continuous random variables with bounded support and use it to provide a notion of…

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.…

A multidimensional nonnegative matrix is called polystochastic if the sum of its entries over each line is equal to $1$. The permanent of a multidimensional matrix is the sum of products of entries over all diagonals. We prove that if $d$…

The subject of the present paper are stability properties of the solution set to set-valued inclusions. The latter are problems emerging in robust optimization and mathematical economics, which can not be cast in traditional generalized…

For interval polynomial matrices, we identify the minimal testing set, whose stability can guarantee that of the whole uncertain set. Our results improve the conclusions given by Kamal and Dahleh.

This paper is concerned with exponential stability of a class of infinite dimensional coupled systems. It is proved that under some admissibility conditions, the considered infinite dimensional coupled system is governed by a…