Given a two-dimensional fractional multiplicative process (Ft)t∈[0,1] determined by two Hurst exponents H1 and H2, we show that there is an associated uniform Hausdorff dimension result for the images of subsets of [0, 1] by F if and only if H1 = H2.

While the presence of long-range dependence in the asset returns seems to be a stylized fact, the issue of arguing the possible causes of this phenomena is totally obscure. Trying to shed light in this problem, we investigate the possible sources of the long-range dependence phenomena in the Brazilian Stock Market. For this purpose, we employ a sample which comprises stocks traded in the Brazil...

In this paper, we build an estimator of the Hurst exponent of a fractional Lévy motion. The stochastic process is observed with random noise errors in the following framework: continuous time and discrete observation times. In both cases, we prove consistency of our wavelet type estimator. Moreover we perform some simulations in order to study numerically the asymptotic behaviour of this estimate.

Integration with respect to a fractional Brownian motion with Hurst parameter 1/2 < H < 1 is related to the inner product: (f, g)H = H(2H − 1) ∫

Let B(t), t ∈ [−1, 1], be the fractional Brownian motion with Hurst parameter H ∈ ( 1 2 , 1 ) . In this paper we present the series representation

This paper investigates the effect of the 2008 financial crisis on informational efficiency by carrying out a long-memory analysis of European corporate bond markets. We compute the Hurst exponent for fifteen sectorial indices to scrutinise the time-varying behaviour of long-range memory, applying a shuffling technique to avoid short-term correlation. We find that the financial crisis has uneve...

In this paper linear stochastic evolution equations driven by infinite-dimensional fractional Brownian motion are studied. A necessary and sufficient condition for the existence and uniqueness of the solution is established and the spatial regularity of the solution is analyzed; separate proofs are required for the cases of Hurst parameter above and below 1/2. The particular case of the Laplaci...