Convergence of Scaled Renewal Processes to Fractional Brownian Motion

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

Weak convergence to the fractional Brownian sheet in Besov spaces

In this paper we study the problem of the approximation in law of the fractional Brownian sheet in the topology of the anisotropic Besov spaces. We prove the convergence in law of two families of processes to the fractional Brownian sheet: the first family is constructed from a Poisson procces in the plane and the second family is defined by the partial sums of two sequences of real independent...

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...

Berry-Esseen bound for MLE for linear stochastic differential equations driven by fractional Brownian motion

We investigate the rate of convergence of the distribution of the maximum likelihood estimator (MLE) of an unknown parameter in the drift coefficient of a stochastic process described by a linear stochastic differential equation driven by a fractional Brownian Motion (fBM). As a special case, we obtain the rate of convergence for the case of the fractional Ornstein-Uhlenbeck type process studie...

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory