We consider a growth collapse model in a random environment for which the input rates might depend on the state of an underlying irreducible Markov chain and at state change epochs there is a possible downward jump to a level that is a random fraction of the level just before the jump. The distributions of these jumps are allowed to depend on both the originating and target states. Under a very weak assumption we develop an explicit formula for the conditional moments (of all orders) of the time stationary distribution. We then consider special cases and show how to use this result to study a growth collapse process in which the times between collapses have a phase-type distribution.
|Original language||American English|
|Number of pages||9|
|Journal||Probability in the Engineering and Informational Sciences|
|State||Published - Jan 2010|
Bibliographical noteFunding Information:
O. Kella was supported in part by grant No. 964/06 from the Israel Science Foundation and the Vigevani Chair in Statistics.