Related papers: Estimation of the Memory Parameter of the Infinite…
The result provided in this paper helps complete a unified picture of the scaling behavior in heavy-tailed stochastic models for transmission of packet traffic on high-speed communication links. Popular models include infinite source…
We consider a change-point test based on the Hill estimator to test for structural changes in the tail index of Long Memory Stochastic Volatility time series. In order to determine the asymptotic distribution of the corresponding test…
This paper deals with the problem of inference associated with linear fractional diffusion process with random effects in the drift. In particular we are concerned with the maximum likelihood estimators (MLE) of the random effect…
The infinite servers queue with Poisson arrivals state transient probabilities, considering the time origin at the beginning of a busy period, mean and variance monotony as time functions is studied. These studies, for which results it is…
To perform a queuing analysis or design in a communications context, we need to estimate the values of the input parameters, specifically the mean of the arrival rate and service time. In this paper, we propose an approach for estimating…
We establish the averaging property for a queuing process with one server, M(t)/GI/1. It is a new relation between the output flow rate and the input flow rate, crucial in the study of the Poisson Hypothesis. Its implications include the…
In certain applications, for instance biomechanics, turbulence, finance, or Internet traffic, it seems suitable to model the data by a generalization of a fractional Brownian motion for which the Hurst parameter $H$ is depending on the…
The fractional stable motion is a prototypical stochastic process exhibiting both heavy tails and long-range dependence, parameterized via a stability index $\alpha$ and a Hurst exponent $H$. We consider a nonstationary extension where the…
We analyze the largest eigenvalue statistics of m-dependent heavy-tailed Wigner matrices as well as the associated sample covariance matrices having entry-wise regularly varying tail distributions with parameter $0<\alpha<4$. Our analysis…
In many complex systems studied in statistical physics, inter-arrival times between events such as solar flares, trades and neuron voltages follow a heavy-tailed distribution. The set of event times is fractal-like, being dense in some time…
The queue system,with Poisson arrivals,constant service time and infinite servers, busy period distribution is intensively studied because, due to its probability density function quite easy interpretation, it may serve as a clue to…
A univariate Hawkes process is a simple point process that is self-exciting and has clustering effect. The intensity of this point process is given by the sum of a baseline intensity and another term that depends on the entire past history…
Internet traffic exhibits self-similarity and long-range dependence (LRD) on various time scales. A well studied issue is the estimation of statistical parameters characterizing traffic self-similarity and LRD, such as the Hurst parameter…
In this paper, we show how the sampling properties of the Hurst exponent methods of estimation change with the presence of heavy tails. We run extensive Monte Carlo simulations to find out how rescaled range analysis (R/S), multifractal…
The Hurst exponent is a significant metric for characterizing time sequences with long-term memory property and it arises in many fields. The available methods for estimating the Hurst exponent can be categorized into time-domain and…
Experimentally observed networks of interacting dynamical systems are inferred from recorded multivariate time series by evaluating a statistical measure of dependence, usually the cross-correlation coefficient, or mutual information. These…
We present methodology for estimating the stochastic intensity of a doubly stochastic Poisson process. Statistical and theoretical analyses of traffic traces show that these processes are appropriate models of high intensity traffic…
Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes. We provide direct evidence that for five human…
Observing a load process above high thresholds, modeling it as a pulse process with random occurrence times and magnitudes, and extrapolating life-time maximum or design loads from the data is a common task in structural reliability…
The goal of this paper is two-fold: 1. We review classical and recent measures of serial extremal dependence in a strictly stationary time series as well as their estimation. 2. We discuss recent concepts of heavy-tailed time series,…