Regularly varying functions

By A. Jessen, Thomas Mikosch. 2006

756 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/350f266d824aa0ee992022036f609b394bea4ce7

How researchers see this paper

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

In Artificial Intelligence

In Management Science and Operations Research

In Mathematical Physics

Citations in the corpus

Sums of Pairwise Quasi-Asymptotically Independent Random Variables with Consistent Variation (2009, background): “See also Lemma 3.1 of Jessen and Mikosch[13] for the extension of Lemma 2.1 of Davis and Resnick[7] to real-valued random variables.”
Conditioning on an extreme component: Model consistency with regular variation on cones (2008, background): “RVρ The class of regularly varying functions with index ρ; see [1,6,10,29,32].”
Regularly Varying Measures on Metric Spaces: Hidden Regular Variation and Hidden Jumps (2013, neutral): “See, for instance, [8, 16, 17, 19, 20, 24, 26, 37, 40, 42, 46].”
Limit Laws for Random Vectors with an Extreme Component (2005, background): “nce to types theorem. Consider the following cases. 1. ρ>0: For this case, we have β∈RV ρ and there exists β˜(t)∈RV ρ such that β˜(·) is continuous, strictly increasing to ∞ with β∼β˜. (See, e.g., [38].) So without loss of generality, for the case ρ>0, we may assume β(·) is continuous and stri”
Asymptotics of random contractions (2010, background): “See Jessen and Mikosch (2006), Denisov and Zwart (2007), and Resnick (2007) for details on Breiman’s lemma and for some of its generalisations.”
Multivariate extremes and the aggregation of dependent risks: examples and counter-examples (2009, neutral): “A brief and very readable introduction to the field is found in Mikosch (2004).”
Asymptotic properties of estimators in a stable Cox–Ingersoll–Ross model (2013, background): “As in the proof of Lemma 3.12 in Jessen and Mikosch (2006), we obtain (3.15) from (3.18).”
Singular phenomena in nonlinear elliptic problems. From blow-up boundary solutions to equations with singular nonlinearities (2006, background): “For details on the below properties, we refer to Seneta [85].”
Tail Risk and Asset Prices (2014, background): “Further details and derivations are found in Jessen and Mikosch (2006).”
Estimation of extreme risk regions under multivariate regular variation (2011, background): “In this paper we consider, much more general, multivariate regularly varying distributions [for a review, see Jessen and Mikosch (2006)].”
Stable limits for sums of dependent infinite variance random variables (2009, background): “By a multivariate version of a result of Breiman (8) (see Basrak et al. (5)) it follows that the first term on the right-hand side of (4.6) inherits the regular variation from X0 with index α and by a standard argument (see Jessen and Mikosch (36), Lemma 3.12) it follows that (X1, . . . , Xd) and th”
Stochastic model for ultraslow diffusion (2006, background): “In this section we outline some interesting connections between fractional calculus, anomalous diffusion models in physics, and the stochastic processes studied in this paper.”
Asymptotics for Weighted Random Sums (2011, background): “6 can be found in [14] for a regularly varying number of summands, N , Ci ≡ 1, and nonnegative {Xi} with lighter tails than N .”
Threefold Introduction to Fractional Derivatives (2008, background): “3] There is a close relationship to the theory of regularly varying functions [107] as evidenced by the following result [52].”