Related papers: Complete convergence theorem for stationary heavy …

In this article, we consider the basic contact process in a static random environment on the half space $Z^d\times Z^+$ where the recovery rates are constants and the infection rates are independent and identically distributed random…

We study almost sure limiting behavior of extreme and intermediate order statistics arising from strictly stationary sequences. First, we provide sufficient dependence conditions under which these order statistics converges almost surely to…

We study the persistence probability for some discrete-time, time-reversible processes. In particular, we deduce the persistence exponent in a number of examples: first, we deal with random walks in random sceneries (RWRS) in any dimension…

We prove a convergence theorem for partial sums of sectorial forms with vertex zero and a common semi-angle. As an example we prove an absorption theorem for sectorial forms.

In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.

Temporal difference (TD) learning with linear function approximation (linear TD) is a classic and powerful prediction algorithm in reinforcement learning. While it is well-understood that linear TD converges almost surely to a unique point,…

We show that a large class of stationary continuous-time regenerative processes are finitarily isomorphic to one another. The key is showing that any stationary renewal point process whose jump distribution is absolutely continuous with…

In this paper, we give rates of convergence in the strong invariance principle for non-adapted sequences satisfying projective criteria. The results apply to the iterates of ergodic automorphisms T of the d-dimensional torus, even in the…

This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions. More precisely, we deal with random fields of the form $X_k =…

Statistical inference for non-stationary data is hindered by the failure of classical central limit theorems (CLTs), not least because there is no fixed Gaussian limit to converge to. To resolve this, we introduce relative weak convergence,…

The aim of this paper is to establish a strong convergence theorem for a strongly nonexpansive sequence in a Banach space. We also deal with some applications of the convergence theorem.

The paper investigates uniform convergence of wavelet expansions of Gaussian random processes. The convergence is obtained under simple general conditions on processes and wavelets which can be easily verified. Applications of the developed…

We give some details about the stationary phase lemma. We first prove a special case where the high order terms are derived explicitly. Based on that, we prove a more general case by using Morse lemma.

We give a substitute to Feller property for semigroups of time-changed processes; under some conditions this leads to establish sufficient (new) conditions for the semigroups to be Feller. Moreover, given a standard process and a sequence…

Modeling univariate block maxima by the generalized extreme value distribution constitutes one of the most widely applied approaches in extreme value statistics. It has recently been found that, for an underlying stationary time series,…

The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to…

In this paper we prove a rate of convergence for the continuous time filtering solution of a multiple timescale correlated nonlinear system to a lower dimensional filtering equation in the limit of large timescale separation. Correlation is…

For a stationary sequence that is regularly varying and associated we give conditions which guarantee that partial sums of this sequence, under normalization related to the exponent of regular variation, converge in distribution to a…

We study non-stationary averaging processes, where each term of a sequence is a weighted average of previous terms, namely $a_{n+1} = \sum_{j=1}^n p_n(j) a_j$. Our results extend classical theory in two distinct regimes. First, we prove a…

We present a general black box theorem that ensures convergence of a sequence of stationary Markov processes, provided a few assumptions are satisfied. This theorem relies on a control of the resolvents of the sequence of Markov processes,…