We consider a passive scalar in a periodic shear flow perturbed by an additive fractional noise with the Hurst exponent H ∈ (0, 1). We establish a diffusive homogenization limit for the tracer when the Hurst exponent H ∈ (0, 1/2). We also identify an intermediate range of times when the tracer behaves diffusively even when H ∈ (1/2, 1). The proof is based on an auxiliary limit theorem for an ad...

The fractal scaling properties of the heartbeat time series are studied in a controlled ergometric regime using the Hurst rescaled range R/S analysis. The long-time ”memory effect” quantified by the value of the Hurst exponent H > 0.5 is found to increase during progresive physical activity at healthy subjects in contrast to those having stable angina pectoris (SAP), where it is decreasing. We ...

in this paper, we have estimated the memory of thetehran stock exchange indices. the estimation of fractional differencing parameter is carried out by various methods such as mle, nls, hurst exponent, gph, lo, whittle and wavelet. the estimation results of whittle, wavelet, hurst, and lo methods allow us to conclude that the returns on stock indices (tepix, tedpix, tedix, financial index and in...

Operator fractional Brownian motion (OFBM) is the natural vector-valued extension of the univariate fractional Brownian motion. Instead of a scalar parameter, the law of an OFBM scales according to a Hurst matrix that affects every component of the process. In this paper, we develop the wavelet analysis of OFBM, as well as a new estimator for the Hurst matrix of bivariate OFBM. For OFBM, the un...

Correct and efficient estimation of the Hurst parameter H of long-range dependent (LRD) traffic is important in traffic analysis. The low computational cost and the wavelets’ scale invariance make wavelet transform suitable for analysis of LRD processes. In this thesis, we apply wavelet-based estimation of H to MPEG-1 and MPEG4 encoded video sequences. Frequency-domain estimators (periodogram a...

Methods of contemporary mathematical physics such as chaos theory are useful for analyzing and understanding the behavior of complex biological and physiological systems. The three dimensional model of HIV/AIDS is the basis of active research since it provides a complete characterization of disease dynamics and the interaction of HIV-1 with the immune system. In this work, the behavior of the H...

In this paper we show empirical data from Internet traffic measurements. Collected measurements are analyzed for different protocols, such as TCP and UDP. We perform statistical analysis through the correlation coefficients, covariance, and self-similarity degree i.e. Hurst parameter. Our experimental studies captured traffic with Hurst parameter around 0.7-0.75, which is near half way between ...

The aim of this study is to investigate the effects of sampling rate on Hurst exponents derived from Blood Oxygenation Level Dependent functional Magnetic Resonance Imaging (BOLD fMRI) resting state time series. fMRI measurements were performed on 2 human subjects and a selection of gel phantoms. From these, Hurst exponents were calculated. It was found that low sampling rates induced non-trivi...

In this short paper, we propose a new multi-fractal flow model, aiming to provide a possible explanation for the crossover phenomena that appear in the estimation of Hurst exponent for network traffic. It is shown that crossover occurs if the network flow consists of several components with different Hurst components. Our results indicate that this model might be useful in network traffic model...