We derive the asymptotic behavior of weighted quadratic variations of fractional Brownian motion B with Hurst index H = 1/4. This completes the only missing case in a very recent work by I. Nourdin, D. Nualart and C. A. Tudor. Moreover, as an application, we solve a recent conjecture of K. Burdzy and J. Swanson on the asymptotic behavior of the Riemann sums with alternating signs associated to B.

We consider a queue fed by Gaussian traffic and give conditions on the input process under which the path space large deviations of the queue are governed by the rate function of the fractional Brownian motion. As an example we consider input traffic that is composed of of independent streams, each of which is a fractional Brownian motion, having different Hurst indices.

We consider the problem of efficient estimation for the drift of fractional Brownian motion B := ( B t ) t∈[0,T ] with hurst parameter H less than 1 2 . We also construct superefficient James-Stein type estimators which dominate, under the usual quadratic risk, the natural maximum likelihood estimator.

Dr John Hurst’s approach to the treatment of people with intellectual disabilities was ahead of its time. In the early 1970s, John, who has died aged 79, developed the pre-discharge unit at South Ockenden Hospital, Essex, as a therapeutic community, as well as a number of community group homes. He also introduced one of the earliest community nursing services in intellectual disability there be...

Let B and e B be two independent, d-dimensional fractional Brownian motions with Hurst parameter H ∈ (0, 1) . Assume d ≥ 2. We prove that the intersection local time of B and e B I(BH , e BH) = Z

A positive recurrent, aperiodic Markov chain is said to be long range dependent (LRD) when the indicator function of a particular state is LRD. This happens if and only if the return time distribution for that state has infinite variance. We investigate the question of whether other instantaneous functions of the Markov chain also inherit this property. We provide conditions under which the fun...

A major issue in statistical physics literature is the study of the long range dependence phenomenon usually presented in natural, social and financial processes. In particular, a big part of this literature relies on the determination of a parameter known as the Hurst exponent. Although many methods have been proposed to deal with this task, none of them are suitable for any time series and so...

Selected Writings of Sir Arthur Hurst (1879-1944), ed. by THOMAS HUNT, London, British Society of Gastroenterology, 1970, pp. xiv, 218, illus., £2X00 (E1X50 to members of the Society). Hurst was probably the most original thinker of his contemporary physicians. Indomitable in the face of deafness and chronic asthma he was an iconoclast, destroying long-held beliefs based on flimsy foundations. ...

The Hurst parameter H characterizes the degree of long-range dependence (and asymptotic self-similarity) in stationary time series. Many methods have been developed for the estimation of H from data. In practice, however, the classical estimation techniques can be severely affected by non-stationary artifacts in the time series. In fact, the assumption that the data can be modeled by a stationa...

BACKGROUND Identifying the emotional state is helpful in applications involving patients with autism and other intellectual disabilities; computer-based training, human computer interaction etc. Electrocardiogram (ECG) signals, being an activity of the autonomous nervous system (ANS), reflect the underlying true emotional state of a person. However, the performance of various methods developed ...