Published online by Cambridge University Press: 21 December 2009
We consider a growth collapse model in a random environment for which the inputrates might depend on the state of an underlying irreducible Markov chain and atstate change epochs there is a possible downward jump to a level that is arandom fraction of the level just before the jump. The distributions of thesejumps are allowed to depend on both the originating and target states. Under avery weak assumption we develop an explicit formula for the conditional moments(of all orders) of the time stationary distribution. We then consider specialcases and show how to use this result to study a growth collapse process inwhich the times between collapses have a phase-type distribution.