In this paper, we study the stochastic integration with respect to local times of fractional Brownian motion B with Hurst index 1/2 < H < 1. As a related problem we define the weighted quadratic covariation [f(B), B ] ) of f(B) and B as follows n−1

Osteoporosis is a disease in which low bone mass and microarchitectural deterioration of bone tissue lead to increased bone fragility and a consequent increase in fracture risk. The objective of this paper is to develop and validate a new method to assess bone microarchitecture on radiographs. Taking into account the piecewise fractal nature of bone radiograph images, an appropriate fractal mod...

We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter H > 1/2 and a multidimensional standard Brownian motion. The proof relies on some a priori estimates, which are obtained using the methods of fractional integration, and the c...

Journal: Inflammatory Bowel Disease Manuscript ID: IBD-12-0469 Wiley Manuscript type: Original Research Articles Basic Science Date Submitted by the Author: 26-Jun-2012 Complete List of Authors: Hurst, Roger; University of Chicago, Surgery Pocivavsek, Luka; University of Pittsburg, Surgery Efrati, Efi; University of Chicago, James Franck Institute Lee, Ka; University of Chicago, James Franck In...

Recent traac analyses from various packet networks have shown the existence of long-range dependence in bursty traf-c. In evaluating its impact on queuing performance, earlier investigations have noted how the presence of long-range dependence , or a high value of the Hurst parameter H, is often associated with surprisingly large queue sizes. As a result, a common impression has been created of...

Using the multiple stochastic integrals we prove an existence and uniqueness result for a linear stochastic equation driven by the fractional Brownian motion with any Hurst parameter. We study both the one parameter and two parameter cases. When the drift is zero, we show that in the one-parameter case the solution in an exponential, thus positive, function while in the two-parameter settings t...

Over the last few years, the network community has started to make heavy use of novel concepts such as self-similarity and Long-Range Dependence (LRD). Despite their wide use, there is still much confusion regarding the identification of such phenomena in real network traffic data. In this paper, we show that estimating Long-Range Dependence is not straightforward: there is no systematic or def...

The paper represents the research results of studying the switches. The model of a switching link has been suggested. The switch has been presented in the form of a Queuing System (QS), the study of dynamic characteristics of switches has been undertaken and the adequacy of the proposed model of a switching link to actual switches has been valued. The maximum error of the modelling is no more t...

Let q ≥ 2 be a positive integer, B be a fractional Brownian motion with Hurst index H ∈ (0, 1), Z be an Hermite random variable of index q, and Hq denote the Hermite polynomial having degree q. For any n ≥ 1, set Vn = ∑n−1 k=0 Hq(Bk+1 − Bk). The aim of the current paper is to derive, in the case when the Hurst index verifies H > 1 − 1/(2q), an upper bound for the total variation distance betwee...

In this paper we show a decomposition of the bifractional Brownian motion with parameters H,K into the sum of a fractional Brownian motion with Hurst parameter HK plus a stochastic process with absolutely continuous trajectories. Some applications of this decomposition are discussed.