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Natural disasters may have considerable impact on society as well as on (re)insurance industry. Max-stable processes are ideally suited for the modeling of the spatial extent of such extreme events, but it is often assumed that there is no temporal dependence. Only a few papers have introduced spatio-temporal max-stable models, extending the Smith, Schlather and Brown-Resnick spatial processes. These models suffer from two major drawbacks: time plays a similar role as space and the temporal dynamics is not explicit. In order to overcome these defects, we introduce spatio-temporal max-stable models where we partly decouple the influence of time and space in their spectral representations. We introduce both continuous and discrete-tim
Max-stable processes are central models for spatial extremes. In this paper, we focus on some space-time max-stable models introduced in Embrechts et al. (2016). The processes considered induce discrete-time Markov chains taking values in the space o
The risk of extreme environmental events is of great importance for both the authorities and the insurance industry. This paper concerns risk measures in a spatial setting, in order to introduce the spatial features of damages stemming from environme
Partially motivated by the recent papers of Conus, Joseph and Khoshnevisan [Ann. Probab. 41 (2013) 2225-2260] and Conus et al. [Probab. Theory Related Fields 156 (2013) 483-533], this work is concerned with the precise spatial asymptotic behavior for
We derive concentration inequalities for functions of the empirical measure of large random matrices with infinitely divisible entries and, in particular, stable ones. We also give concentration results for some other functionals of these random matr
Electromagnetic pulses are typically treated as space-time (or space-frequency) separable solutions of Maxwells equations, where spatial and temporal (spectral) dependence can be treated separately. In contrast to this traditional viewpoint, recent a