کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1155764 958765 2012 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Conditions for the existence of quasi-stationary distributions for birth–death processes with killing
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Conditions for the existence of quasi-stationary distributions for birth–death processes with killing
چکیده انگلیسی

We consider birth–death processes on the nonnegative integers, where {1,2,…}{1,2,…} is an irreducible class and 0 an absorbing state, with the additional feature that a transition to state 0 (killing) may occur from any state. Assuming that absorption at 0 is certain we are interested in additional conditions on the transition rates for the existence of a quasi-stationary distribution. Inspired by results of Kolb and Steinsaltz [M. Kolb, D. Steinsaltz, Quasilimiting behavior for one-dimensional diffusions with killing, Ann. Probab. 40 (2012) 162–212] we show that a quasi-stationary distribution exists if the decay rate of the process is positive and exceeds at most finitely many killing rates. If the decay rate is positive and smaller than at most finitely many killing rates then a quasi-stationary distribution exists if and only if the process one obtains by setting all killing rates equal to zero is recurrent.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 122, Issue 6, June 2012, Pages 2400–2410
نویسندگان
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