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^*

^*Corresponding author for this work

School of Statistics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	576-599
Number of pages	24
Journal	Advances in Applied Probability
Volume	41
Issue number	2
DOIs	https://doi.org/10.1239/aap/1246886624
State	Published - 2009

Keywords

Extinction
Generalized Jiřina process
Geometric series

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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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AU - Li, Yuqiang

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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

U2 - 10.1239/aap/1246886624

DO - 10.1239/aap/1246886624

M3 - 文章

AN - SCOPUS:70350287785

SN - 0001-8678

VL - 41

SP - 576

EP - 599

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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Keywords

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