Related papers: Random sampling of long-memory stationary processe

From a continuous-time long memory stochastic process, a discrete-time randomly sampled one is drawn. We investigate the second-order properties of this process and establish some time-and frequency-domain asymptotic results. We mainly…

A statistical model of discrete finite length random processes with negative power law spectral densities is presented. The definition of terms is followed by a description of the spectral density trend. An algorithmic construction of…

In this article, we aim to further clarify certain subtle aspects of processes that exhibit long memory in the second-order sense. We construct a long-memory stochastic sequence, in the sense that the series of absolute autocovariances…

Long memory or long range dependency is an important phenomenon that may arise in the analysis of time series or spatial data. Most of the definitions of long memory of a stationary process $X=\{X_1, X_2,\cdots,\}$ are based on the…

In this paper we consider the problem of measuring stationarity in locally stationary long-memory processes. We introduce an $L_2$-distance between the spectral density of the locally stationary process and its best approximation under the…

In this paper we study the convergence to fractional Brownian motion for long memory time series having independent innovations with infinite second moment. For the sake of applications we derive the self-normalized version of this theorem.…

Extreme events are an important theme in various areas of science because of their typically devastating effects on society and their scientific complexities. The latter is particularly true if the underlying dynamics does not lead to…

The large deviations of an infinite moving average process with exponentially light tails are very similar to those of an i.i.d. sequence as long as the coefficients decay fast enough. If they do not, the large deviations change…

Lifelong language learning seeks to have models continuously learn multiple tasks in a sequential order without suffering from catastrophic forgetting. State-of-the-art approaches rely on sparse experience replay as the primary approach to…

We propose a stochastic process driven by memory effect with novel distributions including both exponential and leptokurtic heavy-tailed distributions. A class of distribution is analytically derived from the continuum limit of the discrete…

Pathways of diffusion observed in real-world systems often require stochastic processes going beyond first-order Markov models, as implicitly assumed in network theory. In this work, we focus on second-order Markov models, and derive an…

We simulate static memory materials on a two-dimensional lattice. The bulk properties of such materials depend on boundary conditions. Considerable information can be stored in various local patterns. We observe local probabilities…

In this paper we give simple sufficient conditions for linear type processes with short memory that imply the invariance principle. Various examples including projective criterion are considered as applications. In particular, we treat the…

This paper studies seasonal long-memory processes with Gegenbauer-type spectral densities. Estimates for singularity location and long-memory parameters based on general filter transforms are proposed. It is proved that the estimates are…

Shearing a disordered or amorphous solid for many cycles with a constant strain amplitude can anneal it, relaxing a sample to a steady state that encodes a memory of that amplitude. This steady state also features a remarkable stability to…

We obtain the rate of growth of long strange segments and the rate of decay of infinite horizon ruin probabilities for a class of infinite moving average processes with exponentially light tails. The rates are computed explicitly. We show…

Identifying and quantifying memory are often critical steps in developing a mechanistic understanding of stochastic processes. These are particularly challenging and necessary when exploring processes that exhibit long-range correlations.…

We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification, are important because they are relatively easy to simulate. One does not…

We propose a stochastic process driven by the memory effect with novel distributions which include both exponential and leptokurtic heavy-tailed distributions. A class of the distributions is analytically derived from the continuum limit of…

We investigate power spectra of a randomly sampled stationary stochastic signal, e.g. a spatial component of a turbulent velocity. We extend the methods of previous authors that basically assumed point or delta function sampling by…