کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4625855 1631774 2016 20 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Constructing transient birth–death processes by means of suitable transformations
ترجمه فارسی عنوان
ساختن فرآیند مرگ و میر گذرا با استفاده از تحولات مناسب
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
چکیده انگلیسی

For a birth–death process N(t) with a reflecting state at 0 we propose a method able to construct a new birth–death process M(t) defined on the same state-space. The birth and death rates of M(t) depend on the rates of N(t) and on the probability law of the process N(t) evaluated at an exponentially distributed random time. Under a suitable assumption we obtain the conditional probabilities, the mean of the process, and the Laplace transforms of the downward first-passage-time densities of M(t). We also discuss the connection between the proposed method and the notion of ν-similarity, as well as a relation between the distribution of M(t) and the steady-state probabilities of N(t) subject to catastrophes governed by a Poisson process. We investigate new processes constructed from (i) a birth–death process with constant rates, and (ii) a linear immigration-death process. Various numerical computations are performed to illustrate the obtained results.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 281, 30 April 2016, Pages 152–171
نویسندگان
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