کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10527184 | 958721 | 2015 | 28 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Max-stable processes and stationary systems of Lévy particles
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We study stationary max-stable processes {η(t):tâR} admitting a representation of the form η(t)=maxiâN(Ui+Yi(t)), where âi=1âδUi is a Poisson point process on R with intensity eâudu, and Y1,Y2,⦠are i.i.d. copies of a process {Y(t):tâR} obtained by running a Lévy process for positive t and a dual Lévy process for negative t. We give a general construction of such Lévy-Brown-Resnick processes, where the restrictions of Y to the positive and negative half-axes are Lévy processes with random birth and killing times. We show that these max-stable processes appear as limits of suitably normalized pointwise maxima of the form Mn(t)=maxi=1,â¦,nξi(sn+t), where ξ1,ξ2,⦠are i.i.d. Lévy processes and sn is a sequence such that snâ¼clogn with c>0. Also, we consider maxima of the form maxi=1,â¦,nZi(t/logn), where Z1,Z2,⦠are i.i.d. Ornstein-Uhlenbeck processes driven by an α-stable noise with skewness parameter β=â1. After a linear normalization, we again obtain limiting max-stable processes of the above form. This gives a generalization of the results of Brown and Resnick (1977) to the totally skewed α-stable case.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 125, Issue 11, November 2015, Pages 4272-4299
Journal: Stochastic Processes and their Applications - Volume 125, Issue 11, November 2015, Pages 4272-4299
نویسندگان
Sebastian Engelke, Zakhar Kabluchko,