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 {c
n
}, 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.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Cited by
1 articles.
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1. L2limits of generalized Jiřina processes;Statistics & Probability Letters;2017-10