Simulation of Brown–Resnick processes

By Marco Oesting, Zakhar Kabluchko, Martin Schlather. 2012

73 citations recorded by the source corpus.

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.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/03e9d576be295725b9d190d0161bf8c418f034a2

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Citations in the corpus

Spatial extremes: Max-stable processes at work (2013, background): “A particularly well known example is the case of Brown–Resnick processes and, although more sophisticated strategies are possible Oesting et al. (2012), a simple yet efficient Journal de la Société Française de Statistique, Vol. 154 No. 2 156-177 http://www.sfds.asso.fr/journal © Société Française…”
Generalized Pickands constants and stationary max-stable processes (2016, methodology): “ for Hδ W holds. This is a fruitful observation since there is active research on the simulation of max-stable processes (Dieker and Mikosch, 2015; Dombry et al., 2016) and even of the constant Cδ W (Oesting et al., 2012). We conclude this section with several examples. GENERALIZED PICKANDS CONSTANT”
Geostatistics of Dependent and Asymptotically Independent Extremes (2013, methodology): “Furthermore, methods for simulating Brown–Resnick processes have been developed (Oesting et al. 2012; Schlather 2002; Ribatet 2011), though they are more computationally intensive than for the Schlather or Smith models.”