Abstract
Let X(t) denote the size of a certain population at time t **2267 0. It is assumed that at times when no catastrophes occur, the population grows according to the differential equation
. The hazard function for the occurrence of a catastrophe is β(X(t)), i.e.
. If a catastrophe or downward jump takes place at time T, then it is assumed that
, where h is a given function. The problem will be to study the distribution of X(t), especially as t → ∞.
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© 1985 Springer-Verlag Berlin Heidelberg
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Gripenberg, G. (1985). Stationary Distributions for Populations Subject to Random Catastrophes. In: Capasso, V., Grosso, E., Paveri-Fontana, S.L. (eds) Mathematics in Biology and Medicine. Lecture Notes in Biomathematics, vol 57. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93287-8_8
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DOI: https://doi.org/10.1007/978-3-642-93287-8_8
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