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Estimation of the self-similarity parameter in linear fractional stable motion
Simulation results indicate that both the "power" and "log" estimators work well when α > 1, and the estimator based on the discrete linear filter works well also when α ≤ 1. Expand
Conditional sampling for spectrally discrete max-stable random fields
Max-stable random fields play a central role in modeling extreme value phenomena. We obtain an explicit formula for the conditional probability in general max-linear models, which include a largeExpand
On the ergodicity and mixing of max-stable processes
Max-stable processes arise in the limit of component-wise maxima of independent processes, under appropriate centering and normalization. In this paper, we establish necessary and sufficientExpand
On the wavelet spectrum diagnostic for Hurst parameter estimation in the analysis of Internet traffic
This work explores the use of the wavelet spectrum, whose slope is commonly used to estimate the Hurst parameter of long-range dependence, and shows that much more than simple slope estimates are needed for detecting important traffic features. Expand
Simulation methods for linear fractional stable motion and farima using the fast fourier transform
We present efficient methods for simulation, using the Fast Fourier Transform (FFT) algorithm, of two classes of processes with symmetric α-stable (SαS) distributions. Namely, (i) the linearExpand
How rich is the class of multifractional Brownian motions
The multifractional Brownian motion (MBM) processes are locally self-similar Gaussian processes. They extend the classical fractional Brownian motion processes by allowing their self-similarityExpand
Extremal stochastic integrals: a parallel between max-stable processes and α-stable processes
We construct extremal stochastic integrals$$\ {\, \int^{\!\!\!\!\!\!e}_{E}} f(u) M_\alpha(du)$$ of a deterministic function $$f(u)\ge 0$$ with respect to a random $$\alpha-$$Fréchet ($$\alpha>0$$)Expand
Inference for dynamic and latent variable models via iterated, perturbed Bayes maps
A new theoretical framework for iterated filtering is developed and an algorithm supported by this theory displays substantial numerical improvement on the computational challenge of inferring parameters of a partially observed Markov process. Expand
Stochastic properties of the linear multifractional stable motion
We study a family of locally self-similar stochastic processes Y = {Y(t)} t∈ℝ with α-stable distributions, called linear multifractional stable motions. They have infinite variance and may possessExpand
On the structure and representations of max-stable processes
We develop classification results for max-stable processes, based on their spectral representations. The structure of max-linear isometries and minimal spectral representations play important roles.Expand