Related papers: A weak convergence result for sequential empirical…
We develop inference procedures robust to general forms of weak dependence. The procedures utilize test statistics constructed by resampling in a manner that does not depend on the unknown correlation structure of the data. We prove that…
Looking at bivariate copulas from the perspective of conditional distributions and considering weak convergence of almost all conditional distributions yields the notion of weak conditional convergence. At first glance, this notion of…
The aim of this paper is to give a simpler, more usable sufficient condition to the regularity of generic weakly stationary time series. Also, this condition is used to show how regular processes satisfying these sufficient conditions can…
The empirical copula process plays a central role for statistical inference on copulas. Recently, Segers (2011) investigated the asymptotic behavior of this process under non-restrictive smoothness assumptions for the case of i.i.d. random…
In this article we establish two fundamental results for the sublevel set persistent homology for stationary processes indexed by the positive integers. The first is a strong law of large numbers for the persistence diagram (treated as a…
In this paper, a special sequence of controlled branching processes is considered. We provide a simple set of sufficient conditions for the weak convergence of such processes to a weak solution to a kind of continuous branching processes…
In this paper, we develop a new mathematical technique which allows us to express the joint distribution of a Markov process and its running maximum (or minimum) through the marginal distribution of the process itself. This technique is an…
A notion of evolutionary $\Gamma$-convergence of weak type is introduced for sequences of operators acting on time-dependent functions. This extends the classical definition of $\Gamma$-convergence of functionals due to De Giorgi. The…
Empirical process theory for i.i.d. observations has emerged as a ubiquitous tool for understanding the generalization properties of various statistical problems. However, in many applications where the data exhibit temporal dependencies…
Necessary and sufficient conditions for weak and vague convergence of measures are important for a diverse host of applications. This paper aims to give a comprehensive description of the relationship between the two modes of convergence…
We obtain weak rates for approximation of an integral functional of a Markov process by integral sums. An assumption on the process is formulated only in terms of its transition probability density, and, therefore, our approach is not…
We study the asymptotic behavior of empirical processes generated by measurable bounded functions of an infinite source Poisson transmission process when the session length have infinite variance. In spite of the boundedness of the…
We prove that an iterated function system of similarities on $\mathbb{R}$ that satisfies the weak separation condition and has an interval as its self-similar set satisfies the stronger generalized finite type condition. It is unknown if…
In this paper, we consider a wide class of time-varying multivariate causal processes which nests many classic and new examples as special cases. We first prove the existence of a weakly dependent stationary approximation for our model…
Conditions are given under which the empirical copula process associated with a random sample from a bivariate continuous distribution has a smaller asymptotic covariance function than the standard empirical process based on observations…
We have recently defined a weak Markovian bisimulation equivalence in an integrated-time setting, which reduces sequences of exponentially timed internal actions to individual exponentially timed internal actions having the same average…
We prove a weak-strong convergence result for functionals of the form $\int_{\mathbb{R}^N} j(x, u, Du)\,dx$ on $W^{1,p}$, along equiintegrable sequences. We will then use it to study cases of equality in the extended Polya-Szeg\"o…
In this paper we introduce a weak version of level and epigraph convergence for level functions on topological spaces. In the particular case of topological groups we are able to define convolutions in the set of level functions and show…
The non-exponential relaxation is shown to result from subordination by inverse tempered \alpha-stable processes. The main feature of tempered \alpha-stable processes is a finiteness of their moments, and the class of random processes…
In order to prove weak convergence of the periodic multiplicative Selmer algorithm we ensure that the periodicity matrix is positive and establish a relation between its entries and eigenvalues. Since we can imply that the limit of these…