A note on approximation to multifractional Brownian motion

Abstract

In this paper, we prove approximations of multifractional Brownian motions with moving-average representations and of those with harmonizable representations in the space of continuous functions on [0, 1]. These approximations are constructed by Poisson processes.

Operator Fractional Brownian Motion and Martingale Differences

“…Many results about weak approximation to fBms have been established recently. See [12,19] and the references therein. We point out that the fBm does not represent a casual time-invariant system as there is no well-defined impulse response function.…”

Approximation to Multifractional Riemann-Liouville Brownian Sheet

“…Some authors have studied weak convergence to multifractional Brownian motions. Dai and Li [7] presented a weak limit theorem for the multifractioan Brownian motion based on a Poisson process. By using Donsker's theorem, Dai [8] showed an approximation of the RL-multifractional Brownian motion in Besov spaces.…”