In this paper we investigate practical problems of fractal characterization of network tra c focusing on the estimation and interpretation of the Hurst parameter. The analysis is based on our measurement study of ATM WAN tra c. We point out that in order to use the fractal characterization framework in practice we are faced with various misleading e ects that can deceive our self-similarity tes...

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.

We analyzed the temporal evolution of the displacement of the center of pressure (COP) during prolonged unconstrained standing (30 min) in non-impaired human subjects. The COP represents the collective outcome of the postural control system and the force of gravity and is the main parameter used in studies on postural control. Our analysis showed that the COP displacement during human standing ...

This paper develops a point impact linear regression model in which the trajectory of a continuous stochastic process, when evaluated at a "sensitive time point", is associated with a scalar response. The proposed model complements and is more interpretable than the functional linear regression approach that has become popular in recent years. The trajectories are assumed to have fractal (self-...

This paper develops a point impact linear regression model in which the trajectory of a continuous stochastic process, when evaluated at a “sensitive time point”, is associated with a scalar response. The proposed model complements and is more interpretable than the functional linear regression approach that has become popular in recent years. The trajectories are assumed to have fractal (self-...

We study theoretically and numerically the kinetics of the coefficient of friction of an elastomer due to abrupt changes of sliding velocity. Numerical simulations reveal the same qualitative behavior which has been observed experimentally on different classes of materials: the coefficient of friction first jumps and then relaxes to a new stationary value. The elastomer is modeled as a simple K...

We consider stochastic flow on Rn driven by fractional Brownian motion with Hurst parameter H ∈ ( 1 2 , 1), and study tangent flow and the growth of the Hausdorff measure of sub-manifolds of Rn as they evolve under the flow. The main result is a bound on the rate of (global) growth in terms of the (local) Hölder norm of the flow.

We consider stochastic flow on Rn driven by fractional Brownian motion with Hurst parameter H ∈ ( 1 2 , 1), and study tangent flow and the growth of the Hausdorff measure of sub-manifolds of Rn as they evolve under the flow. The main result is a bound on the rate of (global) growth in terms of the (local) Hölder norm of the flow.

1. COCKAYNE, E. A., 1927, Proc. Roy. Soc. of Med., Vol. 21, P. 505. 2. CAULK, J. R. L., 1922, Trans. of Amer. Assoc. of Genito-Urinary Surgeonis, Vol. 15, p. 470. 3. BACHRACH, R., 1914, Beit. z. klin. Chir., Vol. 88, p. 279. 4. HURST., A. F., and GAYMER-JONES, J., 1931, Brit. Jour. of Urology, Vol. 2, p. 43. 5. BRAAGSCTI, W. F., 1928, "The Practice of Urology," Philadelphia. 6. HUNTER, R. H., 1...

Let B be a fractional Brownian motion with Hurst parameter H = 1/6. It is known that the symmetric Stratonovich-style Riemann sums for ∫ g(B(s)) dB(s) do not, in general, converge in probability. We show, however, that they do converge in law in the Skorohod space of càdlàg functions. Moreover, we show that the resulting stochastic integral satisfies a change of variable formula with a correcti...