کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10527371 | 958840 | 2005 | 32 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Conditional convergence to infinitely divisible distributions with finite variance
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
We obtain new conditions for partial sums of an array with stationary rows to converge to a mixture of infinitely divisible distributions with finite variance. More precisely, we show that these conditions are necessary and sufficient to obtain conditional convergence. If the underlying Ï-algebras are nested, conditional convergence implies stable convergence in the sense of Rényi. From this general result we derive new criteria expressed in terms of conditional expectations, which can be checked for many processes such as m-conditionally centered arrays or mixing arrays. When it is relevant, we establish the weak convergence of partial sum processes to a mixture of Lévy processes in the space of cadlag functions equipped with Skorohod's topology. The cases of Wiener processes, Poisson processes and Bernoulli distributed variables are studied in detail.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 115, Issue 5, May 2005, Pages 737-768
Journal: Stochastic Processes and their Applications - Volume 115, Issue 5, May 2005, Pages 737-768
نویسندگان
Jérôme Dedecker, Sana Louhichi,