Related papers: Functional central limit theorem for heavy tailed …

We prove a functional limit theorem for vector-valued functionals of the fractional Ornstein-Uhlenbeck process, providing the foundation for the fluctuation theory of slow/fast systems driven by such a noise. Our main contribution is on the…

We prove limit theorems of an entirely new type for certain long memory regularly varying stationary infinitely divisible random processes. These theorems involve multiple phase transitions governed by how long the memory is. Apart from one…

There has been recent interest in the conditional central limit question for (strictly) stationary, ergodic processes $...,X_{-1},X_0,X_1,...$ whose partial sums $S_n=X_1+...+X_n$ are of the form $S_n=M_n+R_n$, where $M_n$ is a square…

We give a generalization of the ergodic theorem for semi-Markov linear-type processes. This generalization is proved for the case when a common support of distributions defining this process is not arithmetic. Also we give an uniform…

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 study functional limit theorems for linear type processes with short memory under the assumption that the innovations are dependent identically distributed random variables with infinite variance and in the domain of attraction of stable…

We prove functional limit theorems for dynamical systems in the presence of clusters of large values which, when summed and suitably normalised, get collapsed in a jump of the limiting process observed at the same time point. To keep track…

This paper establishes a functional stable central limit theorem for a class of superdiffusive solutions to stochastic differential equations driven by an $\alpha$-stable process.

In this paper, we establish some functional central limit theorems for a large class of general supercritical superprocesses with spatially dependent branching mechanisms satisfying a second moment condition. In the particular case when the…

We extend to Lipschitz continuous functionals either of the true paths or of the Euler scheme with decreasing step of a wide class of Brownian ergodic diffusions, the Central Limit Theorems formally established for their marginal empirical…

Motivated by applications to the study of depth functions for tree-indexed random variables generated by point processes, we describe functional limit theorems for the intensity measure of point processes. Specifically, we establish uniform…

We establish a new functional central limit theorem result for non-invertible measure preserving maps that are not necessarily ergodic, using the Perron-Frobenius operator. We apply the result to asymptotically periodic transformations and…

In this paper we survey the almost sure central limit theorem and its functional form (quenched) for stationary and ergodic processes. For additive functionals of a stationary and ergodic Markov chain these theorems are known under the…

In this paper, we prove maximal inequalities and study the functional central limit theorem for the partial sums of linear processes generated by dependent innovations. Due to the general weights, these processes can exhibit long-range…

Linear processes are defined as a discrete-time convolution between a kernel and an infinite sequence of i.i.d. random variables. We modify this convolution by introducing decimation, that is, by stretching time accordingly. We then…

We present two limit theorems, a mean ergodic and a central limit theorem, for a specific class of one-dimensional diffusion processes that depend on a small-scale parameter $\varepsilon$ and converge weakly to a homogenized diffusion…

We study the process of suitably normalized successive return times to rare events in the setting of infinite-measure preserving dynamical systems. Specifically, we consider small neighborhoods of points whose measure tends to zero. We…

We study deviation of ergodic averages for dynamical systems given by self-similar tilings on the plane and in higher dimensions. The main object of our paper is a special family of finitely-additive measures for our systems. An asymptotic…

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…

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…