Extinction probability in a birth-death process with killingстатья
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Дата последнего поиска статьи во внешних источниках: 22 декабря 2015 г.
Авторы:
Van Doorn E.A. ,
Zeifman A.I.
Журнал:
Journal of Applied Probability
Том:
42
Номер:
1
Год издания:
2005
Издательство:
Applied Probability Trust
Местоположение издательства:
United Kingdom
Первая страница:
185
Последняя страница:
198
DOI:
10.1239/jap/1110381380
Аннотация:
We study birth-death processes on the nonnegative integers, where 1, 2, . . . is an irreducible class and 0 an absorbing state, with the additional feature that a transition to state 0 may occur from any state. We give a condition for absorption (extinction) to be certain and obtain the eventual absorption probabilities when absorption is not certain. We also study the rate of convergence, as t → ∞, of the probability of absorption at time t, and relate it to the common rate of convergence of the transition probabilities that do not involve state 0. Finally, we derive upper and lower bounds for the probability of absorption at time t by applying a technique that involves the logarithmic norm of an appropriately defined operator. © Applied Probability Trust 2005.
Добавил в систему:
Зейфман Александр Израилевич