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Simulation of Brown-Resnick Processes
Oesting, Marco
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Kabluchko, Zakhar
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Schlather, Martin
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DOI:
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https://doi.org/10.1007/s10687-011-0128-8
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URL:
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http://link.springer.com/article/10.1007/s10687-01...
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Weitere URL:
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https://www.researchgate.net/publication/225731343...
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Dokumenttyp:
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Zeitschriftenartikel
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Erscheinungsjahr:
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2012
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Titel einer Zeitschrift oder einer Reihe:
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Extremes : Statistical Theory and Applications in Science, Engineering and Economics
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Band/Volume:
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15
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Heft/Issue:
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1
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Seitenbereich:
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89-107
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Ort der Veröffentlichung:
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Dordrecht [u.a.]
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Verlag:
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Springer Science + Business Media
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ISSN:
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1386-1999 , 1572-915X
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Sprache der Veröffentlichung:
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Englisch
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Einrichtung:
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Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik > Applied Stochastics (Schlather 2012-)
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Fachgebiet:
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310 Statistik
510 Mathematik
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Freie Schlagwörter (Englisch):
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Error estimate, Extremes, Gaussian process, Max-stable process, Poisson point process
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Abstract:
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Brown–Resnick processes form a flexible class of stationary max-stable
processes based on Gaussian random fields. With regard to applications, fast and
accurate simulation of these processes is an important issue. In fact, Brown–Resnick
processes that are generated by a dissipative flow do not allow for good finite approximations
using the definition of the processes. On large intervals we get either huge
approximation errors or very long operating times. Looking for solutions of this problem,
we give different representations of the Brown–Resnick processes—including
random shifting and a mixed moving maxima representation—and derive various
kinds of finite approximations that can be used for simulation purposes. Furthermore,
error bounds are calculated in the case of the original process by Brown and
Resnick (J Appl Probab 14(4):732–739, 1977). For a one-parametric class of Brown–
Resnick processes based on the fractional Brownian motion we perform a simulation
study and compare the results of the different methods concerning their approximation
quality. The presented simulation techniques turn out to provide remarkable
improvements.
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