Related papers: A functional non-central limit theorem for multipl…

We prove a functional central limit theorem for partial sums of symmetric stationary long range dependent heavy tailed infinitely divisible processes with a certain type of negative dependence. Previously only positive dependence could be…

We establish a new class of functional central limit theorems for partial sum of certain symmetric stationary infinitely divisible processes with regularly varying L\'{e}vy measures. The limit process is a new class of symmetric stable…

Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non-Gaussian stable random variable. A functional version…

We provide a framework for empirical process theory of locally stationary processes using the functional dependence measure. Our results extend known results for stationary Markov chains and mixing sequences by another common possibility to…

We provide a functional central limit theorem for a broad class of smooth functions for possibly noncausal multivariate linear processes with time-varying coefficients. Since the limiting processes depend on unknown quantities, we propose a…

We consider a class of stationary processes exhibiting both long-range dependence and heavy tails. Separate limit theorems for sums and for extremes have been established recently in literature with novel objects appearing in the limits. In…

In this article we derive a self-normalized functional limit theorem for strictly stationary linear processes with i.i.d. heavy-tailed innovations and random coefficients under the condition that all partial sums of the series of…

This article considers multivariate linear processes whose components are either short- or long-range dependent. The functional central limit theorems for the sample mean and the sample autocovariances for these processes are investigated,…

We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…

In this paper, we focus on studying central limit theorems for functionals of some specific stationary random processes. In classical probability theory, it is well-known that for non-linear functionals of stationary Gaussian sequences, we…

We derive a functional limit theorem for the partial maxima process based on a long memory stationary $\alpha$-stable process. The length of memory in the stable process is parameterized by a certain ergodic-theoretical parameter in an…

We consider functionals of long-range dependent Gaussian sequences with infinite variance and obtain nonstandard limit theorems. When the long-range dependence is strong enough, the limit is a Hermite process, while for weaker long-range…

We propose a discrete-time, finite-state stationary process that can possess long-range dependence. Among the interesting features of this process is that each state can have different long-term dependency, i.e., the indicator sequence can…

We investigate a family of discrete-time stationary processes defined by multiple stable integrals and renewal processes with infinite means. The model may exhibit behaviors of short-range or long-range dependence, respectively, depending…

\noindent The paper establishes weak convergence in $C[0,1]$ of normalized stochastic processes, generated by Toeplitz type quadratic functionals of a continuous time Gaussian stationary process, exhibiting long-range dependence. Both…

We provide an empirical process theory for locally stationary processes over nonsmooth function classes. An important novelty over other approaches is the use of the flexible functional dependence measure to quantify dependence. A…

Tests for structural breaks in time series should ideally be sensitive to breaks in the parameter of interest, while being robust to nuisance changes. Statistical analysis thus needs to allow for some form of nonstationarity under the null…

We establish the central limit theorem for linear processes with dependent innovations including martingales and mixingale type of assumptions as defined in McLeish [Ann. Probab. 5 (1977) 616--621] and motivated by Gordin [Soviet Math.…

In order to obtain functional limit theorems for heavy tailed stationary processes arising from dynamical systems, one needs to understand the clustering patterns of the tail observations of the process. These patterns are well described by…

In this paper we develop non-stationary martingale techniques for dependent data. We shall stress the non-stationary version of the projective Maxwell-Woodroofe condition, which will be essential for obtaining maximal inequalities and…