Long-range dependence characteristics have been observed in many natural or physical phenomena. In particular, a significant impact on data network performance has been shown in several papers. Congested Internet situations, where TCP/IP buffers start to fill, show long-range dependent (LRD) self-similar chaotic behaviour. The exponential growth of the number of servers, as well as the number o...

The United States Supreme Court has considered the question of whether a judge or a jury must make the findings necessary to support imposition of the death penalty in several notable cases, including Spaziano v. Florida (1984), Hildwin v. Florida (1989), and Ring v. Arizona (2002). In 2016, the U.S. Supreme Court revisited the subject in Hurst v. Florida Florida Statute § 921.141 allows the ju...

We investigate the local fractal properties of the financial time series based on the evolution of the Warsaw Stock Exchange Index (WIG) connected with the largest developing financial market in Europe. Calculating the local Hurst exponent for the WIG time series we find an interesting dependence between the behavior of the local fractal properties of the WIG time series and the crashes appeara...

We investigate the sharp large deviation properties of the energy and the maximum likelihood estimator for the Ornstein-Uhlenbeck process driven by a fractional Brownian motion with Hurst index greater than one half. A.M.S. Classification: 60F10, 60G15, 60J65

In order to distinguish different morphogenic fields automatically, fractional Brownian motion is used in this paper and the Hurst parameter is used as an important measure to distinguish different morphogenic fields in embryo of zebra fish.

The purpose of this paper is to provide a complete description the convergence in distribution of two subsequences of the signed cubic variation of the fractional Brownian motion with Hurst parameter H = 1/6.