Theory and applications of long-range dependence

By Paul Doukhan, Georges Oppenheim, Murad S. Taqqu. 2003

863 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/785f1d3d3517a078ba5ca02bb79f2b3f988a2a4e

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Citations in the corpus

Polynomial type large deviation inequalities and quasi-likelihood analysis for stochastic differential equations (2011, unknown): “Then for some constant C ′ = C ′(C, p, C p+1) < ∞ independent of h and the sequence Fj , P ⎡ ⎣ sup j=1,...,n ∣∣∣∣∣∣ j∑ i=1 Fi ∣∣∣∣∣∣ p⎤ ⎦ ≤ C ′ [ (nh−1)p/2 + nh1−p ] for all n ∈ N. Proof We use a Rosenthal type inequality for mixing sequences (Rio 1994 or Doukhan et al. 2003).”
Simultaneous estimation of the parameters of the Hurst–Kolmogorov stochastic process (2011, background): “…to describe this behaviour, which was further developed by Mandelbrot and van Ness (1968) and has been known as simple scaling stochastic model or fractional Gaussian noise (see Beran 1994; Embrechts and Maejima 2002; Palma 2007; Doukhan et al. 2003; Robinson 2003; and the references therein).”
A GENERALIZED PORTMANTEAU TEST FOR INDEPENDENCE BETWEEN TWO STATIONARY TIME SERIES (2008, background): “In the past two decades, a great deal of research has been conducted on long memory time series, and its importance has been recognized in both applied and theoretical time series literature (Doukhan, Oppenheim, and Taqqu, 2003; Robinson, 2003; Teyssiére and Kirman, 2005).”
Bibliography on stable distributions, processes and related topics (2004, background): “Dudley, R. (1967). The sizes of compact subsets of Hilbert space and continuity of Gaussian processes.”
Integral representations and properties of operator fractional Brownian motions (2011, background): “FBM plays an important role in both theory and applications, especially in connection with long-range dependence [11, 12].”
Intermittent process analysis with scattering moments (2013, background): “The decay of monomial wavelet moments across scales can be related to the distributions of pointwise Holder exponents [3, 19, 32, 36, 37].”
Fractional Lévy processes with an application to long memory moving average processes (2006, methodology): “We can define a parametric family of FBMs in terms of the stochastic Weyl integral (see Doukhan et al. 2003: Part A; Samorodnitsky and Taqqu 1994: Section 7.2).”