The DOI matches its Crossref record; 49 of the 50 references it cites were found in a registry or an index.
Regularly varying functions
Open accessAbstract
We consider some elementary functions of the components of a regularly varying random vector such as linear combinations, products, minima, maxima, order statistics, powers. We give conditions under which these functions are again regularly varying, possibly with a different index.
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“It has become common knowledge that the in-degree and PageRank of the Web follow a power law with the same exponent (see [14], [26], [32], and [37]).”
From Asymptotic analysis for personalized Web search (2010) · cites this paper as [14]
In the citing paper
“Note that the asymptotic equivalence P (R > x) ∼ C ′ N P (N > x) as x → ∞ holds if we assume that the values of the PageRank R can be approximated by cN E ( 1 /D) , as proposed in [14].”
From Asymptotic analysis for personalized Web search (2010) · cites this paper as [14]
Citations
Cites
An introduction to probability theory and its applications
(1958) · Journal of the Franklin Institute · doi:10.1016/0016-0032(58)90688-4 · Cited by 29,621
Time Series: Theory and Methods
Ziegel, E. R., Brockwell, P. J., & Davis, R. A. (1992) · Technometrics · doi:10.2307/1270070 · Cited by 5,071
Stable Non-Gaussian Random Processes
Samorodnitsky, G. P., & Taqqu, M. S. (2017) · Routledge eBooks · doi:10.1201/9780203738818 · Cited by 4,152
Modelling of extremal events in insurance and finance
Paul Embrechts, A., & Schmidli, H. (1994) · Mathematical Methods of Operations Research · doi:10.1007/bf01440733 · Cited by 3,575
Extreme Values, Regular Variation and Point Processes
Resnick, S. I. (1987) · Springer series in operations research/Springer series in operations research and financial engineering · doi:10.1007/978-0-387-75953-1 · Cited by 3,149
Ledoux, M., & Talagrand, M. (1991) · Springer eBooks · doi:10.1007/978-3-642-20212-4 · Cited by 2,493
Sums of independent random variables
Körner, T. W. (1988) · Cambridge University Press eBooks · doi:10.1017/cbo9781107049949.052 · Cited by 1,768
On the self-similar nature of Ethernet traffic
Leland, W. E., Taqqu, M. S., Willinger, W., & Wilson, D. V. (1993) · ACM SIGCOMM Conference (SIGCOMM) · doi:10.1145/166237.166255 · Cited by 1,117
Random difference equations and Renewal theory for products of random matrices
Kesten, H. (1973) · Acta Mathematica · doi:10.1007/bf02392040 · Cited by 975
Limit theorems of probability theory
Dorogovtsev, A. A., Silvestrov, D. S., Skorokhod, A. V., & Yadrenko, M. I. (2011) · Translations of mathematical monographs · doi:10.1090/mmono/163/05 · Cited by 621
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Metadata
- Authors
- Jessen, H., & Mikosch, T.
- Affiliations
- Laboratory of Actuarial Mathematics, University of Copenhagen, Copenhagen, Denmark
- University of Copenhagen (DK)
- ORCID
- Mikosch, Thomas
- Venue
- Publications de l'Institut Mathematique
- Publisher
- National Library of Serbia
- Published
- 2006
- Volume
- 80
- Issue
- 94
- Pages
- 171-192
- ISSN
- 0350-1302 (ISSN-L)
- 1820-7405
- OpenAlex
- W1984074210
- Cited by
- 236
- References
- 50
- Citations by year
- 2026: 1 · 2025: 11 · 2024: 9 · 2023: 10 · 2022: 17 · 2021: 15 · 2020: 16 · 2019: 9 · 2018: 10 · 2017: 8 · 2016: 8 · 2015: 15 · 2014: 16 · 2013: 17 · 2012: 15
- FWCI
- 7.55
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Publications de l Institut Mathematique (publishedVersion)
- Funders
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Social Sciences › Decision Sciences › Management Science and Operations Research › Probability and Risk Models
- Physical Sciences › Mathematics › Applied Mathematics › Approximation Theory and Sequence Spaces
- Keywords
- regularly varying functions, linear combinations, product, extreme values, order statistics
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