Rate Optimality of Wavelet Series Approximations of Fractional Brownian Motion

72 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Sample Path Properties of Anisotropic Gaussian Random Fields (2009, background): “Ayache and Taqqu [5] derived an optimal wavelet series expansion for fractional Brownian sheet B 0 ; see also [33; 59] for other optimal series expansions for B 0 .”
Geometric Properties of Fractional Brownian Sheets (2007, background): “The results in (2) and (3) describe the geometric and Fourier analytic properties of B .”
Wavelet-Type Expansion of the Rosenblatt Process (2004, background): “Note also that, though it is not stated explicitly, the convergence in (1.8) proved by Meyer et al. [22] holds in the sense analogous to the above: the series in k converge almost surely and uniformly on compact intervals in (1.8) and then the same convergence holds for the series in j . The joint c”
Rates of contraction of posterior distributions based on Gaussian process priors (2008, background): “For these rate-optimal expansions, (4.2) is fulﬁlled as soon as the number of terms in the expansion satisﬁes K = K n (cid:8) Cn 1 /( 2 α) for a large constant C .”
MULTIFRACTIONAL PROCESSES WITH RANDOM EXPONENT (2005, methodology): “5 of [3]) and the inequality a+ b ≤ ab which holds for all reals a ≥ 2 and b ≥ 2, we have that ∑”