We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

D-Norms | SpringerLink

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Skip to main content
SpringerLink
Log in

D-Norms

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

  • First Online:
Multivariate Extreme Value Theory and D-Norms

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

  • 1104 Accesses

Abstract

This chapter is devoted to the theory of D-norms, a topic that is of unique mathematical interest. It is aimed at compiling contemporary knowledge on D-norms. For a survey of the various aspects that are dealt with in Chapter 1 we simply refer the reader to the table of contents of this book.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 59.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Balkema, A. A., and Resnick, S. I. (1977). Max-infinite divisibility. J. Appl. Probab. 14, 309–319. doi:10.2307/3213001.

    Article  MathSciNet  Google Scholar 

  • Billingsley, P. (1999). Convergence of Probability Measures. Wiley Series in Probability and Statistics, 2nd ed. Wiley, New York. doi:10.1002/9780470316962.

    MATH  Google Scholar 

  • Bolley, F. (2008). Separability and completeness for the Wasserstein distance. In Séminaire de Probabilités XLI (C. Donati-Martin, M. Émery, A. Rouault, and C. Stricker, eds.), Lecture Notes in Mathematics, vol. 1934, 371–377. Springer, Berlin. doi:10.1007/978-3-540-77913-1 17.

    Google Scholar 

  • Brown, B. M., and Resnick, S. I. (1977). Extreme values of independent stochastic processes. J. Appl. Probab. 14, 732–739. doi:10.2307/3213346.

    Article  MathSciNet  Google Scholar 

  • Fuller, T. (2016). An Approach to the D-Norms with Functional Analysis. Master’s thesis, University of Würzburg, Germany.

    Google Scholar 

  • de Haan, L., and Ferreira, A. (2006). Extreme Value Theory: An Introduction. Springer Series in Operations Research and Financial Engineering. Springer, New York. doi:10.1007/0-387-34471-3 See http://people.few.eur.nl/ldehaan/EVTbook.correction.pdf and http://home.isa.utl.pt/~anafh/corrections.pdf for corrections and extensions.

  • de Haan, L., and Resnick, S. (1977). Limit theory for multivariate sample extremes. Probab. Theory Related Fields 40, 317–337. doi:10.1007/BF00533086.

    Google Scholar 

  • Hofmann, D. (2009). Characterization of the D-Norm Corresponding to a Multivariate Extreme Value Distribution. Ph.D. thesis, University of Würzburg. http://opus.bibliothek.uni-wuerzburg.de/volltexte/2009/4134/.

  • Huser, R., and Davison, A. C. (2013). Composite likelihood estimation for the Brown-Resnick process. Biometrika 100, 511–518. doi:10.1093/biomet/ass089.

    Article  MathSciNet  Google Scholar 

  • Jarchow, H. (1981). Locally Convex Spaces. Teubner, Stuttgart. doi:10.1007/978-3-322-90559-8.

    Book  Google Scholar 

  • Kabluchko, Z., Schlather, M., and de Haan, L. (2009). Stationary max-stable fields associated to negative definite functions. Ann. Probab. 37, 2042–2065. doi:10.1214/09-AOP455.

    Article  MathSciNet  Google Scholar 

  • Krupskii, P., Joe, H., Lee, D., and Genton, M. G. (2018). Extreme-value limit of the convolution of exponential and multivariate normal distributions: Links to the Hüsler-Reiß distribution. J. Multivariate Anal. 163, 80–95. doi:10.1016/j.jmva.2017.10.006.

    Article  MathSciNet  Google Scholar 

  • Lang, S. (1987). Linear Algebra. 3rd ed. Springer, New York. doi:10.1007/978-1-4757-1949-9.

    Book  Google Scholar 

  • Lax, P. D. (2002). Functional Analysis. Wiley, New York.

    Google Scholar 

  • Molchanov, I. (2005). Theory of Random Sets. Probability and Its Applications. Springer, London. doi:10.1007/1-84628-150-4.

    Google Scholar 

  • Molchanov, I. (2008). Convex geometry of max-stable distributions. Extremes 11, 235–259. doi:10.1007/s10687-008-0055-5.

    Article  MathSciNet  Google Scholar 

  • Ng, K. W., Tian, G.-L., and Tang, M.-L. (2011). Dirichlet and Related Distributions. Theory, Methods and Applications. Wiley Series in Probability and Statistics. Wiley, Chichester, UK. doi:10.1002/9781119995784.

    Book  Google Scholar 

  • Phelps, R. R. (2001). Lectures on Choquet’s Theorem. 2nd ed. Springer, Berlin-Heidelberg. doi:10.1007/b76887.

    MATH  Google Scholar 

  • Reiss, R.-D. (1989). Approximate Distributions of Order Statistics: With Applications to Nonparametric Statistics. Springer Series in Statistics. Springer, New York. doi:10.1007/978-1-4613-9620-8.

    Book  Google Scholar 

  • Ressel, P. (2013). Homogeneous distributions - and a spectral representation of classical mean values and stable tail dependence functions. J. Multivariate Anal. 117, 246–256. doi:10.1007/978-1-4613-9620-8.

    Book  Google Scholar 

  • Revuz, D., and Yor, M. (1999). Continuous Martingales and Brownian Motion. Grundlehren der mathematischen Wissenschaften, 3rd ed. Springer, London. doi:10.1007/978-3-662-21726-9.

    Book  Google Scholar 

  • Rockafellar, R. T. (1970). Convex Analysis. Princeton University Press, New Jersey.

    Google Scholar 

  • Takahashi, R. (1987). Some properties of multivariate extreme value distributions and multivariate tail equivalence. Ann. Inst. Stat. Math. 39, 637–647. doi:10.1007/BF02491496.

    Article  MathSciNet  Google Scholar 

  • Takahashi, R. (1988). Characterizations of a multivariate extreme value distribution. Adv. in Appl. Probab. 20, 235–236. doi:10.2307/1427279.

    Article  MathSciNet  Google Scholar 

  • Vatan, P. (1985). Max-infinite divisibility and max-stability in infinite dimensions. In Probability in Banach Spaces V: Proceedings of the International Conference held in Medford, USA, July 16, 1984 (A. Beck, R. Dudley, M. Hahn, J. Kuelbs, and M. Marcus, eds.), Lecture Notes in Mathematics, vol. 1153, 400–425. Springer, Berlin. doi:10.1007/BFb0074963.

    Google Scholar 

  • Villani, C. (2009). Optimal Transport. Old and New, Grundlehren der mathematischen Wissenschaften, vol. 338. Springer, Berlin. doi:10.1007/978-3-540-71050-9.

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fakultät für Mathematik und Informatik, Universität Würzburg, Würzburg, Germany

    Michael Falk

Authors
  1. Michael Falk
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Falk, M. (2019). D-Norms. In: Multivariate Extreme Value Theory and D-Norms. Springer Series in Operations Research and Financial Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-03819-9_1

Download citation

Publish with us

Policies and ethics

Search

Navigation