Extremal behavior of regularly varying stochastic processes

By Henrik Hult, Filip Lindskog. 2005

115 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/f046785e8f4007842419bff0e32f5113c5c22052

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Citations in the corpus

Regularly varying functions (2006, background): “The following result due to Hult and Lindskog [24], see also Resnick [52, Section 7.3], yields an extension of Lemma 3.1 to regularly varying vectors.”
State-dependent importance sampling for regularly varying random walks (2008, background): “Recently, Hult and Lindskog (2005) and Hult et al. (2005) have developed sample path large deviations for regularly varying processes and other results that parallel some of the development reached by the light-tailed counterpart.”
Functional regular variations, Pareto processes and peaks over threshold (2015, background): “Connections with functional regular variations are well known, see e.g. Hult and Lindskog [13, 14] or Davis and Mikosch [6].”
Efficient inference and simulation for elliptical Pareto processes (2013, background): “Complementary results were provided by Hult & Lindskog (2005) and Davis & Mikosch (2008), using functional regular variation.”
Extremal stochastic integrals: a parallel between max-stable processes and α-stable processes (2005, background): “Giné, Hahn and Vatan (1990) and, recently, de Haan and Lin (2001, 2003) and Hult and Lindskog (2005) use a different perspective of exponent measures on the spaces of paths to handle the laws of max–infinitely divisible and max–stable processes.”
REGULAR VARIATION FOR MEASURES ON METRIC SPACES (2006, methodology): “In the space D([0, 1];R) of càdlàg functions the framework of regularly varying measures has been employed to study the extremal behavior of heavy-tailed stochastic processes and the tail behavior of functionals of their sample paths (see [13] and [15]).”
Regularly Varying Measures on Metric Spaces: Hidden Regular Variation and Hidden Jumps (2013, background): “tion 5) regular variation of the distribution of a Levy process whose Levy measure is regularly varying: lim t!1t b(t)x;1 = x ;x > 0, for some scaling function b(t) !1. We reproduce the result [22, 24] that the limit measure of regular variation with scaling b(t) on D([0;1];R)rf0gconcentrates on ”
Asymptotic properties of estimators in a stable Cox–Ingersoll–Ross model (2013, background): “The reader may refer to Hult and Lindskog (2005) for more details. Remark 6.6 Let 0 < α < 2 and let {Zt : t ≥ 0} be a one-dimensional α-stable process with Lévy measure ν(dz). It follows from Lemma 2.1 of Hult and Lindskog (2007) that, as n→∞, nP(nZt ∈ ·) v −→ tν(·).”
Functional large deviations for multivariate regularly varying random walks (2005, methodology): “This is a modification of Theorems 13 and 15 in [13] with (n,an) replaced by (γn, λn).”
Copulas: Tales and facts (2006, unknown): “The quantities λB(A) constitute a measure λB on the Borel sets of (R ∪ {∞,−∞}) d\{0} and one necessarily has λB(tA) = t −αλB(A), t > 0, for some α > 0, see Hult and Lindskog [13].”
Functional peaks‐over‐threshold analysis (2020, background): “The study of such functional spaces would require more general notions of convergence than in Hult and Lindskog (2005) and has not been undertaken, so far as we know.”
The extremogram: a correlogram for extreme events (2009, background): “For example, the extremal index θ is less than 1 for a GARCH process, which is indicative of extremal clustering, while θ= 1 for SV processes, indicating no clustering.”