A recently proposed alternative to multifractional Brownian motion (mBm) with random Hurst exponent is studied, which we refer as It\^o-mBm. It shown that It\^o-mBm locally self-similar. In contrast mBm, its pathwise regularity almost unaffected by the roughness of functional parameter. The properties are established via a new polynomial moment condition similar Kolmogorov-Chentsov theorem, all...

The intensity of long-range dependence (LRD) of the communications network traffic can be measured using the Hurst parameter. There are various estimators of Hurst parameter which differ in reliability of their results. Getting reliable estimator can help to improve traffic characterization, performance modelling, planning and engineering of the real networks. This paper deals with the comparis...

The presence of stock market efficiency is a distinctive characteristic of the effectively functioning market economy. Investigation of the market efficiency of seven emerging East-European stock exchanges is carried out as their major stock indices (BELEX15, BET, CROBEX, ISE100, PFTS, RTSI, SOFIX) are studied in respect of long-range dependence (LRD), persistency, and forecasting possibili...

This work puts forward an extended definition of vector fractional Brownian motion (fBm) using a distribution theoretic formulation in the spirit of Gel’fand and Vilenkin’s stochastic analysis. We introduce random vector fields that share the statistical invariances of standard vector fBm (self-similarity and rotation invariance) but which, in contrast, have dependent vector components in the g...

We study space-time fluctuations around a characteristic line for a onedimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are created by averaging previous values with random weights. The fluctuations analyzed occur on the scale n where n is the ratio of macroscopic and microscopic sc...

In the present work we investigate the multiscale nature of the correlations for high frequency data (1 min) in different futures markets over a period of two years, starting on the 1st of January 2003 and ending on the 31st of December 2004. In particular, by using the concept of local Hurst exponent, we point out how the behaviour of this parameter, usually considered as a benchmark for persi...

We characterize the asymptotic behaviour of the weighted power variation processes associated with iterated Brownian motion. We prove weak convergence results in the sense of finite dimensional distributions, and show that the laws of the limiting objects can always be expressed in terms of three independent Brownian motions X, Y and B, as well as of the local times of Y . In particular, our re...