The first part of the paper contains the study of the convergence for some weighted power variations of a fractional Brownian motion B with Hurst index H ∈ (0, 1). The behaviour is different when H < 1/2 and powers are odd, compared with the case when H = 1/2. In the second part, one applies the results of the first part to compute the exact rate of convergence of some approximating schemes ass...

We investigate the escape from a potential well of a test particle driven by fractional Gaussian noise with Hurst exponent 0<H<1. From a numerical analysis we demonstrate the exponential distribution of escape times from the well and analyze in detail the dependence of the mean escape time on the Hurst exponent H and the particle diffusivity D. We observe different behavior for the subdiffusive...

We give a stochastic microscopic modelling of stock markets driven by continuous double auction. If we take into account the mimetic behavior of traders, when they place limit order, our virtual markets shows the power-law tail of the distribution of returns with the exponent outside the Levy stable region, the short memory of returns and the long memory of volatilities. The Hurst exponent of o...

Recent studies on traffic measurement analysis in the various networks have shown that packet traffic exhibits Long Range Dependent properties called Self-Similarity. Some papers reported that Self-Similarity degrades the network performance, such as buffer overflow. Thus, we need new network control considering Self-Similar properties. Network control considering the Self-Similarity requires h...

Traffic aggregation is a basic networking operation that merges separate traffic streams in network switching and cross-connect nodes. This paper discusses the experimental results on a generalized and protocol-independent self-similar traffic generator based on the RPG model of OPNET. The aggregation processes results from merging of multiple traffic traces with various Hurst parameters, where...

Based on measurements in live GPRS networks, the degree of selfsimilarity for the aggregated WAP and WEB traffic is investigated by utilizing six well established Hurst parameter estimators. We show that in particular WAP traffic is long-range dependent and its scaling for time scales below the average page duration is not second order self similar. WAP over UDP can also determine the overall t...

In recent years, numerous publications have identi ed a high number of tra c sources to be of self-similar nature. Such tra c can have a negative impact on traditional queuing systems. This paper presents a call admission control algorithm that uses periodic wavelet analysis applied to tra c measurements to estimate the amount of resources necessary to support a certain set of connections under...