Related papers: Strong approximation of partial sums under depende…

Mixtures of regression are a powerful class of models for regression learning with respect to a highly uncertain and heterogeneous response variable of interest. In addition to being a rich predictive model for the response given some…

Let $(X_t)$ be a discrete time Markov chain on a general state space. It is well-known that if $(X_t)$ is aperiodic and satisfies a drift and minorization condition, then it converges to its stationary distribution $\pi$ at an exponential…

We establish an invariance principle for a general class of stationary random fields indexed by $\mathbb Z^d$, under Hannan's condition generalized to $\mathbb Z^d$. To do so we first establish a uniform integrability result for stationary…

We derive conditions under which random sequences of polarizations (two-point symmetrizations) converge almost surely to the symmetric decreasing rearrangement. The parameters for the polarizations are independent random variables whose…

In 1983, N. Herrndorf proved that for a $\phi$-mixing sequence satisfying the central limit theorem and $\liminf_{n\to\infty}\frac{\sigma^2_n}n>0$, the weak invariance principle takes place. The question whether for strictly stationary…

This note considers the maximal positively invariant set for polynomial discrete time dynamics subject to constraints specified by a basic semialgebraic set. The note utilizes a relatively direct, but apparently overlooked, fact stating…

We consider time-dependent dynamical systems arising as sequential compositions of self-maps of a probability space. We establish conditions under which the Birkhoff sums for multivariate observations, given a centering and a general…

In this paper, we consider a class of nonautonomous multi-scale stochastic partial differential equations with fully local monotone coefficients. By introducing the evolution system of measures for time-inhomogeneous Markov semigroups, we…

We establish a new criterion for exponential mixing of random dynamical systems. Our criterion is applicable to a wide range of systems, including in particular dispersive equations. Its verification is in nature related to several topics,…

This article proposes and analyzes explicit and easily implementable temporal numerical approximation schemes for additive noise-driven stochastic partial differential equations (SPDEs) with polynomial nonlinearities such as, e.g.,…

In a seminal 2005 paper, Haagerup and Thorbj{\o}rnsen discovered that the norm of any noncommutative polynomial of independent complex Gaussian random matrices converges to that of a limiting family of operators that arises from…

This note investigates invariance principles for sums of N(nt) iid radom variables, where n is an integer, t is a positive real number and N(u) is a stochastic process with nonnegative integer values. We show that the sequence of sums of…

We establish two theorems for assessing the accuracy in total variation of multivariate discrete normal approximation to the distribution of an integer valued random vector $W$. The first is for sums of random vectors whose dependence…

For any stationary $\mZ^d$-Gibbs measure that satisfies strong spatial mixing, we obtain sequences of upper and lower approximations that converge to its entropy. In the case, $d=2$, these approximations are efficient in the sense that the…

Let $X$, $X_1$, $X_2$, $...$ be i.i.d. random variables, and let $S_n=X_1+... + X_n$ be the partial sums and $M_n=\max_{k\le n}|S_k|$ be the maximum partial sums. We give the sufficient and necessary conditions for a kind of limit theorems…

In this paper we study precise large deviations for the partial sums of a stationary sequence with a subexponential marginal distribution. Our main focus is on distributions which either have a regularly varying or a lognormal-type tail. We…

We provide a systematic approach to deal with the following problem. Let $X_1,\ldots,X_n$ be, possibly dependent, $[0,1]$-valued random variables. What is a sharp upper bound on the probability that their sum is significantly larger than…

In this paper we show how to apply classical probabilistic tools for partial sums $\sum_{j=0}^{n-1}\varphi\circ\tau^j$ generated by a skew product $\tau$, built over a sufficiently well mixing base map and a random expanding dynamical…

In this paper, we study the strong convergence of an algorithm to solve the variational inequality problem which extends(Thong et al, Numerical Algorithms. 78, 1045-1060 (2018)). We have reduced and refined some of their algorithm's…

We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of…