Abstract
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}, wherecdoes not equal the pseudo-drift parameter atx= 0, cannot estimate the speed of extinction accurately. Then the general case is studied. We determine a group of sufficient conditions such thatXn/cn, with a suitable constantcn, converges almost surely asn→ ∞ 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
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