کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
7549922 | 1489920 | 2018 | 29 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Pointwise estimates for first passage times of perpetuity sequences
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We consider first passage times Ïu=inf{n:Yn>u} for the perpetuity sequence Yn=B1+A1B2+â¯+(A1â¦Anâ1)Bn,where (An,Bn) are i.i.d. random variables with values in R+ÃR. Recently, a number of limit theorems related to Ïu were proved including the law of large numbers, the central limit theorem and large deviations theorems (see Buraczewski et al., in press). We obtain a precise asymptotics of the sequence P[Ïu=loguâÏ], Ï>0, uââ which considerably improves the previous results of Buraczewski et al. (in press). There, probabilities P[ÏuâIu] were identified, for some large intervals Iu around ku, with lengths growing at least as loglogu. Remarkable analogies and differences to random walks (Buraczewski and MaÅlanka, in press; Lalley, 1984) are discussed.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 128, Issue 9, September 2018, Pages 2923-2951
Journal: Stochastic Processes and their Applications - Volume 128, Issue 9, September 2018, Pages 2923-2951
نویسندگان
D. Buraczewski, E. Damek, J. Zienkiewicz,