The speed of extinction for some generalized Jiřina processes

Yuqiang Li

doi:10.1239/aap/1246886624

The speed of extinction for some generalized Jiřina processes

Yuqiang Li^*

^*此作品的通讯作者

统计学院

科研成果: 期刊稿件 › 文章 › 同行评审

3 引用（Scopus）

摘要

The speed of extinction for some generalized Jiřina processes {X_n} is discussed. We first discuss the geometric speed. Under some mild conditions, the results reveal that the sequence {cⁿ}; where c does not equal the pseudo-drift parameter at x = 0, cannot estimate the speed of extinction accurately. Then the general case is studied. We determine a group of sufficient conditions such that X_n/c_n, with a suitable constant c_n, converges almost surely as n → ∞ to a proper, nondegenerate random variable. The main tools used in this paper are exponent martingales and stochastic growth models.

源语言	英语
页（从-至）	576-599
页数	24
期刊	Advances in Applied Probability
卷	41
期	2
DOI	https://doi.org/10.1239/aap/1246886624
出版状态	已出版 - 2009

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title = "The speed of extinction for some generalized Ji{\v r}ina processes",

abstract = "The speed of extinction for some generalized Ji{\v r}ina processes \{Xn\} is discussed. We first discuss the geometric speed. Under some mild conditions, the results reveal that the sequence \{cn\}; where c does not equal the pseudo-drift parameter at x = 0, cannot estimate the speed of extinction accurately. Then the general case is studied. We determine a group of sufficient conditions such that Xn/cn, with a suitable constant cn, converges almost surely as n → ∞ to a proper, nondegenerate random variable. The main tools used in this paper are exponent martingales and stochastic growth models.",

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AB - The speed of extinction for some generalized Jiřina processes {Xn} is discussed. We first discuss the geometric speed. Under some mild conditions, the results reveal that the sequence {cn}; where c does not equal the pseudo-drift parameter at x = 0, cannot estimate the speed of extinction accurately. Then the general case is studied. We determine a group of sufficient conditions such that Xn/cn, with a suitable constant cn, converges almost surely as n → ∞ to a proper, nondegenerate random variable. The main tools used in this paper are exponent martingales and stochastic growth models.

KW - Extinction

KW - Generalized Jiřina process

KW - Geometric series

UR - https://www.scopus.com/pages/publications/70350287785

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JO - Advances in Applied Probability

JF - Advances in Applied Probability

IS - 2

ER -

The speed of extinction for some generalized Jiřina processes

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