ON GENERALIZED MAX-LINEAR MODELS IN MAX-STABLE RANDOM FIELDS 21 Davison, A. C. , Padoan, S. A. , and Ribatet, M. (2012 b ). Statistical mod- eling of spatial extremes. Statist. Sci. 27 , 161–186. doi:10.1214/11-STS376 . Discussed in Cooley and Sain (2012), Gabda et al. (2012), Segers (2012) and Shaby and Reich (2012); rejoinder at Davison et al. (2012 a ). Dombry, C. , ´ Eyi-Minko, F. , and Ribatet, M. (2013). Condi- tional simulation of Brown-Resnick processes. Biometrika 100 , 111–124. doi:10.1093/biomet/ass067 . Falk, M. , Hofmann, M. , and Zott, M. (2015). On generalized max-linear models and their statistical interpolation. J. Appl. Probab. 52 , 736–751. doi:10.1239/jap/1445543843 . Falk, M. , H¨ usler, J. , and Reiss, R.-D. (2011). Laws of Small Numbers: Extremes and Rare Events . 3rd ed. Springer, Basel. doi:10.1007/978-3-0348-0009-9 . Gabda, D. , Towe, R. , Wadsworth, J. , and Tawn, J. (2012). Discussion of “Statistical modeling of spatial extremes” by A. C. Davison, S. A. Padoan and M. Ribatet. Statist. Sci. 27 , 189–192. doi:10.1214/12-STS376B . Gin´e, E. , Hahn, M. , and Vatan, P. (1990). Max-infinitely divisible and max- stable sample continuous processes. Probab. Theory Related Fields 87 , 139–165. doi:10.1007/BF01198427 . de Haan, L. , and Ferreira, A. (2006). Extreme Value Theory: An In- troduction . Springer Series in Operations Research and Financial En- gineering. 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 ex- tremes. Probab. Theory Related Fields 40 , 317–337. doi:10.1007/BF00533086 . Kabluchko, Z. (2009). Spectral representations of sum- and max-stable processes. Extremes 12 , 401–424. doi:10.1007/s10687-009-0083-9 .