Abstract
In this paper, a single product continuous time stochastic inventory model for deteriorating items, driven by a. conditional Poisson process, is suggested. It is assumed the process Z
t
modulating the jump intensities of the Poisson process is a Markov chain. By observing the history of the inventory level, a finite dimensional filter for the conditional distribution of Z
t
is found. Further filters are found when the conditional Poisson process is replaced by an integer-valued random measure with predictable compensator depending on a right-constant sample paths process y
t