On the Long-Range Dependence of Fractional Brownian Motion

On the Convergence of MMPP and Fractional ARIMA Processes with Long-Range Dependence to Fractional Brownian Motion

Though the various models proposed in the literature for capturing the long-range dependent nature of network traac are all either exactly or asymptotically second order self-similar, their eeect on network performance can be very diierent. We are thus motivated to characterize the limiting distributions of these models so that they lead to parsimonious modeling and a better understanding of ne...

Fractional Processes with Long-range Dependence

Abstract. We introduce a class of Gaussian processes with stationary increments which exhibit long-range dependence. The class includes fractional Brownian motion with Hurst parameter H > 1/2 as a typical example. We establish infinite and finite past prediction formulas for the processes in which the predictor coefficients are given explicitly in terms of the MA(∞) and AR(∞) coefficients. We a...

On the Mixed Fractional Brownian Motion

If H = 1/2, BH is the ordinary Brownian motion denoted by B = {Bt, t ≥ 0}. Among the properties of this process, we recall the following: (i) B 0 = 0P-almost surely; (ii) for all t ≥ 0, E((B t )2)= t2H ; (iii) the increments of BH are stationary and self-similar with order H ; (iv) the trajectories of BH are almost surely continuous and not differentiable (see [7]). Let us take a and b as two r...

On the Two - Dimensional Fractional Brownian Motion

We study the two-dimensional fractional Brownian motion with Hurst parameter H > 1 2. In particular, we show, using stochastic calculus , that this process admits a skew-product decomposition and deduce from this representation some asymptotic properties of the motion.

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion