کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1154834 958414 2012 7 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The space-fractional Poisson process
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آمار و احتمال
پیش نمایش صفحه اول مقاله
The space-fractional Poisson process
چکیده انگلیسی

In this paper, we introduce the space-fractional Poisson process whose state probabilities pkα(t), t≥0t≥0, α∈(0,1]α∈(0,1], are governed by the equations (d/dt)pkα(t)=−λα(1−B)αpkα(t), where (1−B)α(1−B)α is the fractional difference operator found in the time series analysis. We explicitly obtain the distributions pkα(t), the probability generating functions Gα(u,t)Gα(u,t), which are also expressed as distributions of the minimum of i.i.d. uniform random variables. The comparison with the time-fractional Poisson process is investigated and finally, we arrive at the more general space–time-fractional Poisson process of which we give the explicit distribution.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Statistics & Probability Letters - Volume 82, Issue 4, April 2012, Pages 852–858
نویسندگان
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