Abstract
We propose an exact simulation method for Brown-Resnick random fields, building on new representations for these stationary max-stable fields. The main idea is to apply suitable changes of measure.
Article PDF
Similar content being viewed by others
References
Brown, B., Resnick, S.I.: Extreme values of independent stochastic processes. J. Appl. Probab. 14, 732–739 (1977)
Buishand, T., de Haan, L., Zhou, C.: On spatial extremes: with applications to a rainfall problem. Ann. Appl. Stat. 2, 624–642 (2008)
Davis, R.A., Klüppelberg, C., Steinkohl, C.: Statistical inference for max-stable processes in space and time. J. Royal Statist. Soc. Ser. B 75, 791–819 (2013)
Dieker, A.B., Yakir, B.: On asymptotic constants in the theory of Gaussian processes. Bernoulli 20, 1600–1619 (2014)
Dombry, C., Éyi-Minko, F., Ribatet, M.: Conditional simulation of max-stable processes. Biometrika 100, 111–124 (2013)
Embrechts, P., Klüppelberg, C., Mikosch, T.: Modelling Extremal Events for Insurance and Finance. Springer, Berlin (1997)
Engelke, S., Kabluchko, Z., Schlather, M.: An equivalent representation of the Brown-Resnick process. Stat. Probab. Lett. 81, 1150–1154 (2011)
de Haan, L.: A spectral representation for max-stable processes. Ann. Probab. 12, 1194–1204 (1984)
de Haan, L., Zhou, C.: On extreme value analysis of a spatial process. REVSTAT 6, 71–81 (2008)
Huser, R., Davison, A.C.: Space-time modelling for extremes. J. Royal Statist. Soc. Ser. B 76, 439–461 (2014)
Kabluchko, Z.: Spectral representations of sum- and max-stable processes. Extremes 12, 401–424 (2009)
Kabluchko, Z., Schlather, M., de Haan, L.: Stationary max-stable fields associated to negative definite functions. Ann. Probab. 37, 2042–2065 (2009)
Kroese, D.P., Botev, Z.I.: Spatial Process Generation. In: Schmidt, V (ed.) Lectures on Stochastic Geometry, Spatial Statistics and Random Fields, vol. II, Analysis, Modeling and Simulation of Complex Structures. Springer-Verlag, Berlin (2013)
Leadbetter, M.R., Lindgren, G., Rootzén, H.: Extremes and Related Properties of Random Sequences and Processes. Springer, Berlin (1983)
Oesting, M., Kabluchko, Z., Schlather, M.: Simulation of Brown-Resnick processes. Extremes 15, 89–107 (2012)
Oesting, M., Schlather, M.: Conditional sampling for max-stable processes with a mixed moving maxima representation. Extremes 17, 157–192 (2014)
Oesting, M., Schlather, M., Zhou, C.: On the normalized spectral representation of max-stable processes on a compact set. Preprint available from arXiv: 1310.1813 (2013)
Piterbarg, V.I.: Asymptotic methods in the theory of gaussian processes and fields. AMS. Trans. Math. Monogr. vol. 148 (1996)
R: The R project for statistical computing; see http://www.r-project.org/. 18 Jan 2015
Schlather, M.: Models for stationary max-stable random fields. Extremes 5, 33–44 (2002)
Xanh, N.X.: Ergodic theorems for subadditive spatial processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete 48, 159–176 (1979)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Dieker, A.B., Mikosch, T. Exact simulation of Brown-Resnick random fields at a finite number of locations. Extremes 18, 301–314 (2015). https://doi.org/10.1007/s10687-015-0214-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10687-015-0214-4
Keywords
- Brown-Resnick random field
- Brown-Resnick process
- Max-stable process
- Gaussian random field
- Extremes
- Pickands’s constant
- Monte Carlo simulation