کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5130142 | 1378661 | 2017 | 22 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Ergodic decompositions of stationary max-stable processes in terms of their spectral functions Ergodic decompositions of stationary max-stable processes in terms of their spectral functions](/preview/png/5130142.png)
We revisit conservative/dissipative and positive/null decompositions of stationary max-stable processes. Originally, both decompositions were defined in an abstract way based on the underlying non-singular flow representation. We provide simple criteria which allow to tell whether a given spectral function belongs to the conservative/dissipative or positive/null part of the de Haan spectral representation. Specifically, we prove that a spectral function is null-recurrent iff it converges to 0 in the Cesà ro sense. For processes with locally bounded sample paths we show that a spectral function is dissipative iff it converges to 0. Surprisingly, for such processes a spectral function is integrable a.s. iff it converges to 0 a.s. Based on these results, we provide new criteria for ergodicity, mixing, and existence of a mixed moving maximum representation of a stationary max-stable process in terms of its spectral functions. In particular, we study a decomposition of max-stable processes which characterizes the mixing property.
Journal: Stochastic Processes and their Applications - Volume 127, Issue 6, June 2017, Pages 1763-1784