کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1152800 | 1489905 | 2010 | 7 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A note on the path to extinction of critical Markov branching processes
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آمار و احتمال
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
For critical Markov branching processes {Zt} with finite variance and with time to extinction T, we obtain the asymptotic behavior of the two processes {ZuT/T,0â¤u<1} and {ZTâu,u>0} as Z0=xââ. These processes were called by Jagers and co-workers the “path to extinction” and the “verge of extinction” respectively. We show that as Z0=xââ, (1) for fixed 0â¤u<1, ZuT/T converges in distribution to a mixture of two exponential random variables; (2) for fixed u>0, ZTâu converges in distribution, and after normalizing by uâ1, the limit further converges to a gamma distribution as uââ. Simulation is used to illustrate the results.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Statistics & Probability Letters - Volume 80, Issues 5â6, 1â15 March 2010, Pages 263-269
Journal: Statistics & Probability Letters - Volume 80, Issues 5â6, 1â15 March 2010, Pages 263-269
نویسندگان
Xiaowei Wu, Marek Kimmel,