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Exact simulation of Brown-Resnick random fields at a finite number of locations. (English) Zbl 1319.60108
Summary: 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.

MSC:
60G60 Random fields
60G70 Extreme value theory; extremal stochastic processes
60G15 Gaussian processes
60G10 Stationary stochastic processes
65C05 Monte Carlo methods
68U20 Simulation (MSC2010)
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References:
[1] Brown, B; Resnick, SI, Extreme values of independent stochastic processes, J. Appl. Probab., 14, 732-739, (1977) · Zbl 0384.60055
[2] Buishand, T; de Haan, L; Zhou, C, On spatial extremes: with applications to a rainfall problem, Ann. Appl. Stat., 2, 624-642, (2008) · Zbl 1273.62258
[3] Davis, RA; Klüppelberg, C; Steinkohl, C, Statistical inference for MAX-stable processes in space and time, J. Royal Statist. Soc. Ser. B, 75, 791-819, (2013) · Zbl 1411.60071
[4] Dieker, AB; Yakir, B, On asymptotic constants in the theory of Gaussian processes, Bernoulli, 20, 1600-1619, (2014) · Zbl 1298.60043
[5] Dombry, C; Éyi-Minko, F; Ribatet, M, Conditional simulation of MAX-stable processes, Biometrika, 100, 111-124, (2013) · Zbl 1316.60078
[6] Embrechts, P., Klüppelberg, C., Mikosch, T.: Modelling Extremal Events for Insurance and Finance. Springer, Berlin (1997) · Zbl 0873.62116
[7] Engelke, S; Kabluchko, Z; Schlather, M, An equivalent representation of the Brown-resnick process, Stat. Probab. Lett., 81, 1150-1154, (2011) · Zbl 1234.60056
[8] de Haan, L, A spectral representation for MAX-stable processes, Ann. Probab., 12, 1194-1204, (1984) · Zbl 0597.60050
[9] de Haan, L; Zhou, C, On extreme value analysis of a spatial process, REVSTAT, 6, 71-81, (2008) · Zbl 1153.62074
[10] Huser, R; Davison, AC, Space-time modelling for extremes, J. Royal Statist. Soc. Ser. B, 76, 439-461, (2014)
[11] Kabluchko, Z, Spectral representations of sum- and MAX-stable processes, Extremes, 12, 401-424, (2009) · Zbl 1224.60120
[12] Kabluchko, Z; Schlather, M; de Haan, L, Stationary MAX-stable fields associated to negative definite functions, Ann. Probab., 37, 2042-2065, (2009) · Zbl 1208.60051
[13] 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) · Zbl 1273.62258
[14] Leadbetter, M.R., Lindgren, G., Rootzén, H.: Extremes and Related Properties of Random Sequences and Processes. Springer, Berlin (1983) · Zbl 0518.60021
[15] Oesting, M; Kabluchko, Z; Schlather, M, Simulation of Brown-resnick processes, Extremes, 15, 89-107, (2012) · Zbl 1329.60157
[16] Oesting, M; Schlather, M, Conditional sampling for MAX-stable processes with a mixed moving maxima representation, Extremes, 17, 157-192, (2014) · Zbl 1312.60071
[17] 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) · Zbl 1431.60042
[18] Piterbarg, V.I.: Asymptotic methods in the theory of gaussian processes and fields. AMS. Trans. Math. Monogr. vol. 148 (1996) · Zbl 0841.60024
[19] R: The R project for statistical computing; see http://www.r-project.org/. 18 Jan 2015 · Zbl 0384.60055
[20] Schlather, M, Models for stationary MAX-stable random fields, Extremes, 5, 33-44, (2002) · Zbl 1035.60054
[21] Xanh, NX, Ergodic theorems for subadditive spatial processes, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 48, 159-176, (1979) · Zbl 0397.60081
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